A Study of Musical Theatre’s Gilbert and Sullivan Essay

Theatre, as we know it, always aims to provoke its audience through emotions, by invoking the muses of comedy and tragedy, and everything else in between. Many names are synonymous to the history and success of theatre, but none comes close to the iconic contributions of Britain’s most illustrious duo, collectively known as Gilbert and Sullivan. Sharp, clever wit and brilliant rhyme have found their rightful places in the theatrical masterpieces composed by renowned playwright William S. Gilbert, and his equally-profound partner, composer Arthur Sullivan. The 1870s marked the beginning of a new ideology in musical theatre, as the partnership brought to the fore previously unheard-of standards that were identified by a mix of intelligence in satire and silliness, as well as melodic instrumentations that complement the passion and creativity of the written word. Such was the success of the outcome that Gilbert and Sullivan managed to pioneer and influence generations of theatre innovations, and eventually, become a solid pillar in both British and American popular culture. Musical comedy writers, Broadway lyricists, literary authors and composers—and even important names in politics and government—are just some of those who have credited Gilbert and Sullivan for a number of their works. Through the excellent vision of production genius Richard D’Oyly Carte, the impressive collaborations of Gilbert and Sullivan were set to stage. The Savoy Theatre in London, Carte’s headquarters, became the setting for many of the duo’s memorable musicals. Innovative from the beginning, The Savoy was the first theatre in the world to utilize electricity, and summoned theatre-goers all over to sample this taste of technology as well as the brilliance of Gilbert and Sullivan’s works, which were later aptly named â€Å"Savoy Operas† (Kenrick, 2000-2003). The Gilbert and Sullivan era spanned from 1871 to 1896, and between them they were able to create fourteen critically-acclaimed and hugely popular masterpieces—counting The Mikado, Pirates of Penzance, and H. M. S. Pinafore as the most widely-received. II. William Gilbert and Arthur Sullivan, The Beginning The young William Gilbert (1836-1911) was the son of a naval surgeon by profession, and a writer by interest. He jumpstarted his son’s juvenile career by allowing the boy to accompany his articles with illustrations; William soon found his own talent for writing, and came up with his own compositions. These writings, called Bab Ballads, would later find their way into some of Gilbert and Sullivan’s most acclaimed musicals. Gilbert’s Bab Ballads were known for their unique use of humor played out through logic (Classic Gilbert and Sullivan). Mike Leigh, English film and theatre director, concludes this style to be decidedly one that had Gilbert’s signature, where the establishment of the strange, absurd, and otherwise unacceptable concept would be expertly formed into perfect examples of reason and truth—all done with a bite of silliness metamorphosing into deadpan prose. On the other hand, the musical inclinations of Arthur Sullivan (1842-1900) also had strong parental influences—his father was a bandmaster with the military, and the then 8-year-old Arthur had already become expert in all the band instruments. In 1856, after concluding his initial attempts of composing songs and anthems in school, Arthur proceeded to claim the first Mendelssohn Prize, and took further studies in composition and conducting at the Royal Academy of Music, as well as in Leipzig. He performed his 1861 graduation piece, an ode to William Shakespeare’s The Tempest, at the Crystal Palace; this earned him the prestige of being heralded as the country’s most promising young composer. Among Sullivan’s applauded works early in his career were The Masque at Kenilworth (1842), The Prodigal Son (1869), On Shore and Sea (1871), and a ballet entitled L’lle Enchantee (1864) (Classic Gilbert and Sullivan). William Gilbert’s and Arthur Sullivan’s paths crossed as they attended a rehearsal of the play Ages Ago, where the composer Frederic Clay made introductions. A couple of years after that, Gilbert and Sullivan made their first foray as co-creators of what would be a uniquely wonderful style admired by the whole world. III. Gilbert and Sullivan and the Comic Opera A staple of English theatre during the Edwardian era, the comic opera’s origins come from 18th-century Naples, in Italy. Known as intermezzi, short comic routines were used to end the bigger acts, and enjoyed much popularity that they were later written to exist on their own. The final output was the comic opera, the concept of which was soon transported to Paris, where it easily claimed the approval of French dramatists and audiences. However, the same could not be said upon its arrival on English territory, for theatre professionals and enthusiasts at the time were still more interested in evolving the popular Ballad Opera and the newer form of Music Hall; the latter was introduced to fill the need for a lighter, less serious entertainment style. Finally, in 1871, the comic opera was launched in London’s Gaiety Theatre, through the production of Thespis; or the Gods Grown Old. This not only marked a new chapter in British theatre, but also the first entry of the long-running collaboration of musical theatre’s most prestigious partnership—Gilbert and Sullivan. It all started with the efforts of John Hollingshead, then manager of the Gaiety Theatre, who employed Gilbert’s expertise to write the libretto of his theatre’s 1871 Christmas musical. They had worked together once before, on the burlesque Robert the Devil which also ran in Gaiety. To complete the requirement for the musical, Hollingshead contacted Sullivan, who was then still inexperienced in stage production. This first encounter produced Thespis, but was initially given much criticism and low confidence in the team. Four years later, the producer Carte would bring them back together to create Trial By Jury; the resulting 300 performances declared it a resounding success, as well as a much-awaited approval of the partnership. Perhaps the foremost appeal of Gilbert and Sullivan’s works had much to do with their ability to poke fun and humor at establishment, as well as current social and political issues. This was a high time for patriotism in Britain, and the British audience’s validation of the comic operas sealed the career success of the duo. Much of the credit would also have to go to the newness of concept and execution of each piece, that even foreign audiences understood and appreciated the essence of every performance. To this day, comic opera will always be defined by Gilbert and Sullivan—they truly made it their niche, and those that attempted to surpass or equal their achievements failed to do so (Gillan, 2007). Of the fourteen collaborative works of the famed partnership, many were lauded as icons of comic opera. These were the celebrated productions of Thespis: or the Gods Grown Old, Trial By Jury (1975), The Sorcerer (1877), and of course, the previously-mentioned The Mikado, Pirates of Penzance, and H. M. S. Pinafore. Thespis: or the Gods Grown Old, being Gilbert and Sullivan’s first collaboration, had no real indications of the phenomenal future awaiting its two creators. Yet the classic Gilbert and Sullivan format was already applied in the work, by setting the opera in the mythical Mount Olympus. In the story, the gods have all grown old and the celestial buildings were all in a state of ruin. Then a group of actors and their leader named Thespis went up the mountain to have a picnic, and noticed the sad condition of the place. Thespis gets into a deal with Jupiter, agreeing that his group would take on the work of the tired gods, provided that Mercury would remain to brief them of their duties. But things do not go as planned, and Mercury only noted all complaints. When the gods on break finally return, they discover the unsatisfactory results and banish the group back to earth. 1875’s Trial By Jury made use of an old legal procedure as the main idea, specifically a ‘breach of promise’ trial. This often took place in earlier times, when a man could be summoned to court and sued for taking back a marriage proposal. The characters included a dashing, worldly bachelor and the woman who called for the hearing, a maiden dressed in wedding attire. An all-male jury and an unscrupulous judge round up the cast, with the woman directing her flirtations toward the jury but would end up receiving a proposal from the judge himself—as a way to resolve the case. The storyline established prevailing comic themes that would later be present in most of Gilbert and Sullivan’s works: (1) true and undying love may come from and end in unexpected sources and directions; (2) the existence of politicians who achieved their public status by charming and lying their way through, and (3) aversion for mature women, specifically those over 40—which is, in truth, a nod to patriarchy and sexism. Two years later, Gilbert and Sullivan produced The Sorcerer, which featured a man of magic who brings chaos and confusion to a tiny English village by creating a love potion. In many ways, The Sorcerer made a satire of class distinction and social propriety, which were standard elements in Victorian society. Yet in true Gilbert and Sullivan style, the output was of inimitable wit and class that the references were not declared offensive at all—so much was its success that aside from its own numerous showings, The Sorcerer was staged even as far as America, albeit unauthorized. And while the opera’s theme could have been translated by the French through a multitude of sexual innuendos and references played out by unreal, fantastic characters, Gilbert and Sullivan designed The Sorcerer with roles that were utterly believable and credible—the kind of people that actually exist in everyday life, that the British audience could identify. The penchant for poking fun at British social conventions became Gilbert and Sullivan’s running objective, and in 1878 they again succeeded in producing a successful show that audiences celebrated. H. M. S. Pinafore once again uses love as a theme, but a deeper reading would reveal that the opera tackles the discussion of England’s class society. With the narrative centering on the daughter of a naval captain’s rejection of the Secretary of the Navy—the highest-ranking man of uniform—for the affections of a common sailor, H. M. S. Pinafore showcases the reality of a person born into a particular class, and the availability of options based on this system. It is also a criticism of their society’s double standard on the issue of marriage; they patronize literature’s ideals about love conquering all, while in real life they disapprove of unions between people of different social classes. This time, audiences were not as forgiving as they were with The Sorcerer—the prevailing adherence and respect for the British class system caused low ticket sales. That, as well as the unrelenting hot weather pulled Gilbert and Sullivan’s celebrity down—for a moment. During Sullivan’s summer concerts, he came up with the smart strategy to include several medleys of his Pinafore score; the result was a revived interest in the opera, and eventually sales and attendance reached phenomenal heights. Such was the success of the opera that it encouraged Carte to involve Gilbert and Sullivan in the actual business, dividing all production expenses and sales profits among the three of them. From this point on, Gilbert and Sullivan were given decision-making authority in all their productions. However, because of the opera’s impact on the British audiences, many unauthorized production of Pinafore were staged, particularly in the United States, where international copyright laws were not yet in place. To assert ownership, Carte brought the production overseas where it enjoyed a brief yet successful run in Broadway, and made sure that Gilbert and Sullivan’s works were covered by copyright laws in the country. Carte had this foremost on his mind when Gilbert and Sullivan came up with yet another opera destined for iconic status, 1880’s Pirates of Penzance. This time, Carte protected the production rights both in Britain and New York, which established the legal precedents still observed today. The move has benefited playwrights and writers all over the world, with this initial case on intellectual property rights. Love as an ideal is again the running theme in Penzance, as the story explores the adventures of a young man named Frederick who, by no choice of his own, worked under the tutelage of a group of pirates. As luck would have it, he falls for the daughter of a Major General—a momentous experience that drove him to make up for his previous deeds by eliminating the pirates he used to be associated with. The pirates in question actually turned out to be noblemen who made the wrong choices in life; in the end, they, including Frederick, all take the Major’s many daughters as their wives. There was no stopping the success of Gilbert and Sullivan, and they forged on to firmly claim their place in popular culture. Several productions were created, among them Patience (1881), which told of the poet’s charm and magnetism, a surefire way to get his way with the women, except for the one he wants—who is but a simple milkmaid. Written as a comedy, Patience ultimately focused on aestheticism, which referred to an artist’s or writer’s obsession with beauty. Carte employed a brilliant marketing strategy to promote the production, with the assistance of famed writer Oscar Wilde. The writer was tasked to do the lecture circuit around the United States, to provide a full background on this new ideology, and to ensure public awareness of the opera. Not surprisingly, this tactic resulted in positive financial reaction. With Patience, Gilbert and Sullivan introduced another innovation, this time with the characters of the opera narrative and the songs assigned to them. In their previous works, the duo’s main goal to put a message across was met; the technical level of the story itself remained the way it was from their early projects. Not the kinds to stay within their comfort zones, Gilbert and Sullivan expanded their competencies as playwrights by integrating the characters with music—producing songs and personalities that were exclusive to each other, and the situations they were in. Comic opera was what people called the Gilbert and Sullivan theatre style; in reality, it was the birth of the integrated musical. The partnership, while perfect on an intellectual realm, was slowly revealing its cracks caused by the personal differences of the two artists. Gilbert was apparently so taken with the love potion plot—which he successfully delivered in The Sorcerer—and wanted to create another opera using the same idea. This was not taken positively by Sullivan, who soon decided, on impulse, to focus more on serious projects. Of course, Gilbert did not take this well either, and the beginning of what would be a personal feud between the two took its place. Carte tried to remedy the situation by staging a rerun of The Sorcerer, only as a stopgap measure for further rifts that may damage company existence and operations. Fate once again played a major role in the succeeding events, because the partnership was saved by a mundane object—a Japanese sword. It fell from the wall of Gilbert’s study and almost hit him, but instead of dismissing the incident, Gilbert took inspiration from it. This set the tone and plot for Gilbert and Sullivan’s most popular opera to date. The Mikado, staged in 1885, carried the same elements that had made the duo famous: love, and social commentary; with a generous helping of humor and wit. The plot itself was hilarious—it was a scenario questioning what would happen when the Emperor of Japan, know as the Mikado, passes a decree declaring flirting as illegal, and punishable by law. The townsfolk of Titipu refused to follow the new ruling, and consequently appointed Koko, a condemned tailor, as Lord High Executioner. Strangely, the condition for this appointment was for Koko to be beheaded, as he was proven guilty of violating the new law, unless he finds someone to behead first. Koko manages to find someone to execute, and that was the traveling minstrel named Nanki-Poo, who actually agrees with Koko only if he is allowed to marry the beautiful Yum-Yum—Koko’s fiance. Nanki-Poo was given a month to enjoy the wedded life before he was beheaded and Koko can finally marry Yum-Yum. But soon an old woman named Katisha appears, a representative of the royal court, and announces that Nanki-Poo is really the crown prince—guilty of the crime, as he had flirted with her and tried to escape execution by hiding in the small town. Eventually, the Mikado himself arrives and declares that his goal for decreeing such an inane ruling was to let the punishment fit the crime. More misunderstandings and deceptions came afterwards, but in the end everyone lives happily ever after. Gilbert and Sullivan decided to use Japan as a setting to create a satire about the British penchant for all things Japanese, during the 1880s. And because it was brilliantly written and the references to British pretensions and petty customs subtle and discreet, audiences failed to make any negative observations and promptly applauded the performance. Exporting The Mikado to the United States was the right thing to do, for it replicated the success of H. M. S. Pinafore and drove Americans into a Japanese frenzy. The Mikado is the sole musical by Gilbert and Sullivan that had been performed in a variety of languages, and is also their only work that spawned a diplomatic controversy. In 1907, the Crown Prince of Japan came over for a state visit, and immediately the British government ordered a ban on The Mikado; only to discover that one of the Prince’s objectives in visiting Britain was to watch the musical. To this day, The Mikado is still widely produced and staged worldwide. However, the problem with having a major success in one’s name is the pressure to produce another one of equal or greater impact. In 1887, Gilbert and Sullivan staged Ruddigore, which entailed more melodrama than their previous collaborations. It truly was an accomplished piece, but audiences kept comparing it with The Mikado. Once more, Sullivan was disheartened by this turn of events and threatened to leave the industry altogether and focus on classical compositions instead. Gilbert tried to change his mind with a new libretto, one that was not an echo of their old work. With The Yeomen of the Guard, an operetta set during the reign of Henry VIII, romance was played out within the constraints of political controversies, as well as the possibility of execution. Sullivan, satisfied with the proposition, proceeded to create a score punctuated with melodrama and emotion, while Gilbert reinvented himself and his style by veering from his usual whimsical comic dialogue. Serious was the best word to use to describe Yeoman, and this became a personal favorite of Sullivan. The monarchy did not escape the sharp wit of the two, either. In 1889, Gilbert and Sullivan resurrected their signature comic style with the staging of The Gondoliers. A story of a couple of anti-royalist gondoliers from Venice who ironically discover that they have suddenly become kings of a country in the midst of a revolution, Gilbert and Sullivan once again mixed fun and comedy to discuss the idiosyncrasies of the royals and the issues of democracy. The Gondoliers became an instant international hit. No less than the public-shy Queen Victoria requested for several private performances of The Gondoliers, which validated the immense contribution of Gilbert and Sullivan to musical theatre. But the personal differences between the two icons continued to get in the way of their professional relationship. Some were serious concerns, yet some were downright trivial—such as the argument over the cost of newly-installed carpets in the Savoy Theatre. Carte and his wife ultimately chose to take Sullivan’s side, which resulted in their production of Ivanhoe, Sullivan’s grand opera. However, this project failed to achieve any semblance of financial success; which was a mirror of Gilbert’s own experience when he went back to writing his own plays. Several years later, the three business partners tried to put everything aside and reconcile, but sadly, they were never able to bring back their glory days. Still, they managed to produce Utopia Limited (1893), another satire of Britain’s unsuccessful efforts in its dealings with other countries; and The Grand Duke (1896), featuring a theatre group’s attempts to claim power in a problematic Germany. Both productions were of the same make and quality as their previous ones, but neither enjoyed substantial performance durations because of expensive production costs. More than that, it was already apparent that Gilbert and Sullivan no longer had the fresh and intriguing style and creativity that had earned them the respect of audiences worldwide (Kenrick, 2000-2003). IV. Reviews Interesting to note are the reviews made for each of Gilbert and Sullivan’s operas, as made by many critics and journalists during the time. Some of the takes of these writers were documented and used as reference, in order to validate the creative contribution given by the duo. One review for Thespis on its opening night in 1871 commended Gilbert and the magnificent storyline he created, as well as the audience’s superb reception of the play. Credits were specifically given to the talent showcased (Perry, 2001). A Trial By Jury review was not truly exciting—while the critic commended the acting and singing done by the performers, it was the â€Å"lateness of the hour† that possibly accounted for the audience’s lackluster reaction (Perry, 2001). H. F. Frost reviewed The Sorcerer in 1877, and emphasized the effective combination of literary merit and dramatic consistency as created by Gilbert and Sullivan, except that their attempts to subtly mix burlesque and opera was not entirely acceptable. Points were given to the theme of exploring human nature’s weaknesses and imperfections (Perry, 2000). It is evident that H. M. S. Pinafore was a huge crowd favorite, as revealed by a review published in 1878. Pinafore was commended for the use of burlesque but had more humor and charm over Trial By Jury and The Sorcerer. The satire and libretto were both noted, and gave Gilbert and Sullivan credit for managing to pull it off without great offense to the public. The actors were also adjudged suited to their roles, and the musical one that will remain in the bills for a long time (Perry, 2001). A review made in 1880 of Pirates of Penzance saw it as having several allusions to H. M. S. Pinafore, particularly in the similarities of some of the characters. But the audience was not put off by that observation, and still applauded the cynicism and wit of Gilbert’s words as well as the charm of Sullivan’s music (Perry, 2000). V. The Final Years Though they never really regained their old camaraderie, Gilbert and Sullivan remained civil to each other until the end. In 1888, Sullivan was granted knighthood, and the former colleagues shared the same stage once more during revivals of their old classics were produced. Later, Sullivan collaborated with other writers to produce several critically-acclaimed operas, including The Emerald Isle in 1900. Sullivan finally passed away at the age of 58, due to a bout of severe bronchitis. Gilbert, on the other hand, got his second wind at the dawn of the new century, with a notable output of librettos and plays. He eventually received his knighthood in 1907, which was long overdue, but allowed him to experience being touted as a British national living treasure. At age 74, while saving a girl from drowning in his own estate, Gilbert was struck by a fatal heart attack. This happened in late May 1911. The great producer Carte succumbed to the permanent effects of illness in 1901, but his opera company was continued by Helen, his wife, and their son Rupert and his wife. They revived the most acclaimed works of Gilbert and Sullivan throughout the years, until the company closed in 1983 due to financial problems. But Bridget, Rupert’s wife, left a considerable amount of money to allow a new group of theatre producers to form a new company, which still stages revivals of the famous musicals of Gilbert and Sullivan to this day. VI. The Gilbert and Sullivan Legacy The achievements of Gilbert and Sullivan were nothing less than national milestones, particularly in the reality of class-conscious Britain. The brilliant wit, humor, and music created by the duo gained popularity with all class levels of society, which was a feat it itself. Apart from that, the team’s theatre philosophy transformed the standard musical preferences to be more attune to popular music, and less concentration on the obscure and exclusive. However, Carte’s company refused to grant performers and directors the freedom to modify each production—every staging had to adhere to the set guidelines of the original team. Critics and audiences could only imagine how fresh eyes and new voices would be able to interpret the tried-and-tested pieces (Wren, 2001). Britain respected the legacy of Gilbert and Sullivan, and their standards of musical theatre bore into all productions made in the late 1800s. George Edwardes, a producer of comic operas, proved to be the duo’s strongest competitor. He started with the success of Dorothy in 1886, which included a ballad entitled â€Å"Queen of My Heart†, that broke all records—even running longer than any of Gilbert and Sullivan’s musicals. But what made Edwardes a respected name was his discovery of a new technique with his production of The Gaiety Girls, a musical named after the famous London theatre. This musical comedy featured many of Gilbert and Sullivan’s standard elements, making it a manifestation of the partnership’s influence on the art. The Gaiety Girls, like most of Gilbert and Sullivan’s operas, carried a theme of love gained and lost. But these musicals only had two general narratives—a poor girl in love with a rich man, and wins him in the end, even in the presence of adversities; and a poor girl who attempts to get out of a marriage she did not want, prompting her to involve other characters on a chase. The music and titles of these musicals all had the same essence, which were really just variations on a theme. Interestingly, the seeming monotony of these musicals were greatly appreciated by the audiences and critics, who preferred them exactly as they were. But these productions could never stand up against the works of Gilbert and Sullivan, particularly those that had traveled to the United States. This fact awakened the British audience from their stupor, as they had to acknowledge the international receipt of their own culture (Morley, 1987). Needless to say, the Gilbert and Sullivan operas consistently received much acclaim from their American audiences; the staging of H. M. S. Pinafore started a nationwide craze aptly called â€Å"Pinafore-mania†. Typical of Americans, the music and songs of Pinafore quickly entered the realm of popular culture, and were included in regular talk. The classic line â€Å"What never? Well, hardly ever! † from Pinafore became standard replies of people all over, and the phrase â€Å"short, sharp stock† that was used in The Mikado to mean â€Å"of severe punishment† was borrowed by various writers, artists, commentators and bands. Perhaps the most celebrated American production of a Gilbert and Sullivan original was Pirates of Penzance, which found its way to Broadway in 1981 and enjoyed a run that broke production and staging records. Gilbert, in particular, would often be cited by popular American writers, such as Johnny Mercer, Larry Hart, Alan Jay Lerner, and Stephen Sondheim. Mercer was even quoted as saying, â€Å"We all come from Gilbert†, and Sondheim made a tribute to the famous librettist in â€Å"Please Hello† from his work Pacific Overtures (1976). It is probably not far-fetched to assume that Gilbert and Sullivan’s work lent sophistication and class to the existing brand of musicals then; soon after, new generations of musical talents appeared, putting the USA on top of the list. The Boston Ideal Opera Company, more popularly known as The Bostonians, made the rounds of theatres all over the country, and were received well for their outstanding performances. They included in the repertoire several original American musicals, but were known for their productions of Gilbert and Sullivan works. A listing of American originals that took after the Gilbert and Sullivan tradition is as follows: El Capitan (1896) by John Philip Sousa The Begum (1887) and Robin Hood (1891) by librettist Harry B, Smith and composer Reginald DeKoven The Highwayman (1897), again by Reginald DeKoven (Gillan, 2007). VII. The Gilbert and Sullivan Influence The influence of Gilbert and Sullivan extended all the way to other forms of art ad communication, which included literary works of famous writers. References to their collaborations are found in the work of writer Isaac Asimov, who wrote a number of stories centered on the puzzles and mysteries of the duo’s operas. One such story was of time travel, where one had to go back in the 1800s to rescue the score to Gilbert and Sullivan’s Thespis (Asimov, 1978). â€Å"The Year of the Action† engaged a debate over the actual date of the action in Pirates of Penzance. A story in Asimov’s famous I, Robot, â€Å"Runaround†, had a character singing parts of songs from Ruddigore, Patience, and Pinafore. Cleverly, Asimov concluded his homage to the duo with his story â€Å"The Up-To-Date Sorcerer†, which was obviously a parody of The Sorcerer. Legendary British author P. G. Wodehouse was also known to cite Gilbert and Sullivan in his writings, and more often exclusively referred to Gilbert. His novels and short stories included numerous allusions to the team’s work, many to Gilbert’s early Bab Ballads (Robinson, 2006). The film industry also found the works of Gilbert and Sullivan great material for a wealth of movies. Many of their musicals were adapted into films, including the actors who originally performed in the theatre versions. The Mikado was adapted into a movie in 1939, in full color, for which it won several awards. Also, many films made use of scores composed for a number of Gilbert and Sullivan musicals, including The Matchmaker (1958), I Could Go On Singing (1963), The Naughty Victorians (1975), The Bad News Bears Go To Japan (1978), Chariots of Fire (1981), The Adventures of Milo and Otis (1989), The Browning Version (1994), and The Hand That Rocks The Cradle (1992). Television is also another medium that has embraced the Gilbert and Sullivan talent. From The Simpsons to Frasier, from Angel to The West Wing, the duo’s music has been showcased in a variety of scenes and episodes. There was even a show dedicated to spoofs of Gilbert and Sullivan musicals, entitled The Star of Christmas. Video games such as Grand Theft Auto: San Andreas also had visual references of Gilbert and Sullivan’s works, particularly of Pirates of Penzance. Outside of media, many personalities in politics also found good material in the team’s celebrated works to promote their platforms and ideologies. A â€Å"short, sharp stock† remains to be a popular mainstay in many manifestos and debates. VIII. On A Personal Level Though their professional partnership was truly accomplished and proven time and again, it was the personal relationship of Gilbert and Sullivan that had suffered the most. Collaborations may or may not be successful if the participants are friends; however, artists like Gilbert and Sullivan probably see no boundaries between who they are and what they do. Sullivan was not rich, and as he grew up he mad it a point to mingle with the rich and influential. He met Gilbert, and immediately discovered the parallels in drive and talent in both of them. However, he also saw something else—that Gilbert’s friendship could be the means for him to make his career flourish. Sullivan had many other powerful friends, including Queen Victoria, who advi

Statistics Chapter 12 Solutions

CHAPTER 12: TESTS FOR TWO OR MORE SAMPLES WITH CATEGORICAL DATA 1. When testing for independence in a contingency table with 3 rows and 4 columns, there are ________ degrees of freedom. a) 5 b) 6 c) 7 d) 12 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test of independence, degrees of freedom 2. If we use the [pic] method of analysis to test for the differences among 4 proportions, the degrees of freedom are equal to: a) 3. b) 4. c) 5. d) 1. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions, degrees of freedom . If we wish to determine whether there is evidence that the proportion of successes is higher in group 1 than in group 2, the appropriate test to use is a) the Z test. b) the [pic]test. c) both of the above d) none of the above ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions 4. If we wish to determine whether there is evidence that the proportion of successes is the same in group 1 as in group 2, the appropriate test to use is a) the Z test. b) the [pic]test. c) both of the above d) none of the above ANSWER: TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions 5. In testing a hypothesis using the [pic] test, the theoretical frequencies are based on the a) null hypothesis. b) alternative hypothesis. c) normal distribution. d) none of the above. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions, properties TABLE 12-1 A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in San Diego County.A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) and (2) seat belt usage (worn or not worn) during the accident. The number of children in each category is given in t he table below. | |Hispanic |Non-Hispanic | |Seat belts worn |31 |148 | |Seat belts not worn |283 |330 | . Referring to Table 12-1, which test would be used to properly analyze the data in this experiment? a) test for independence. b) test for difference between proportions. c) ANOVA F test for interaction in a 2 x 2 factorial design. d) test for goodness of fit. ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: chi-square test of independence 7. Referring to Table 12-1, the calculated test statistic is a) -0. 9991. b) -0. 1368. c) 48. 1849. d) 72. 8063. ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test of independence, test statistic 8.Referring to Table 12-1, at 5% level of significance, the critical value of the test statistic is a) 3. 8415. b) 5. 9914. c) 9. 4877. d) 13. 2767. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test of independence, critical value 9. Referring to Table 12-1, at 5% level of significance, there is sufficient evidence to conclude t hat the a) use of seat belts in motor vehicles is related to ethnic status in San Diego County. b) use of seat belts in motor vehicles depends on ethnic status in San Diego County. c) use of seat belts in motor vehicles is associated with ethnic status in San Diego County. ) all of the above ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: chi-square test of independence, decision, conclusion TABLE 12-2 Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below. |Male Celebrity |Female Celebrity | |Identified product |41 |61 | |Could not identify |109 |89 | 10. Referri ng to Table 12-2, which test would be used to properly analyze the data in this experiment? a) test for independence. b) test for difference between proportions. c) ANOVA F test for main treatment effect. d) test for goodness of fit. ANSWER: a TYPE: MC DIFFICULTY: ModerateKEYWORDS: chi-square test of independence 11. Referring to Table 12-2, the calculated test statistic is a) -0. 1006. b) 0. 00. c) 5. 9418. d) 6. 1194. ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test of independence, test statistic 12. Referring to Table 12-2, at 5% level of significance, the critical value of the test statistic is a) 3. 8415. b) 5. 9914. c) 9. 4877. d) 13. 2767. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test of independence, critical value 13. Referring to Table 12-2, the degrees of freedom of the test statistic are a) 1. b) 2. c) 4. ) 299. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test of independence, degrees of freedom 14. Referring to Table 12-2, at 5 % level of significance, the conclusion is that a) brand awareness of female TV viewers and the gender of the spokesperson are independent. b) brand awareness of female TV viewers and the gender of the spokesperson are not independent. c) brand awareness of female TV viewers and the gender of the spokesperson are related. d) both (b) and (c) ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: chi-square test of independence, decision, conclusion TABLE 12-3A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of a day’s transactions gave the counts shown in the table to each of the 5 memory locations, along with the number of reported errors. |Memory Location: |1 |2 |3 |4 |5 | |Number of Transactions: |82 |100 |74 |92 |102 | |Number of Reported Errors: |11 |12 |6 |9 |10 |The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ. 15. Referring to Table 12-3, which test would be used to properly analyze the data in this experiment? a) test for independence b) test for difference between proportions c) ANOVA F test for main treatment effect d) test for goodness of fit ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions 16. Referring to Table 12-3, the degrees of freedom of the test statistic is a) 4. b) 8. c) 10. d) 448. ANSWER: a TYPE: MC DIFFICULTY: EasyKEYWORDS: chi-square test for difference in proportions, degrees of freedom 17. Referring to Table 12-3, the critical value of the test statistic at 1% level of significance is a) 7. 7794. b) 13. 2767. c) 20. 0902. d) 23. 2093. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions, critical value 18. Referring to Table 12-3, the calculated value of the test statistic is a) -0. 1777. b) -0. 0185. c) 1. 4999. d) 1. 5190. ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: c hi-square test for difference in proportions, test statistic 19. Referring to Table 12-3, at 1% level of significance ) there is sufficient evidence to conclude that the proportions of errors in transactions assigned to each of the 5 memory locations are all different. b) there is insufficient evidence to conclude that the proportions of errors in transactions assigned to each of the 5 memory locations are all different. c) there is sufficient evidence to conclude that the proportion of errors in transactions assigned to each of the 5 memory locations are not all the same. d) there is insufficient evidence to conclude that the proportion of errors in transactions assigned to each of the 5 memory locations are not all the same.ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, decision, conclusion 20. Moving companies are required by the government to publish a Carrier Performance Report each year. One of the descriptive statistics they m ust include is the annual percentage of shipments on which a $50 or greater claim for loss or damage was filed. Suppose two companies, Econo-Move and On-the-Move, each decide to estimate this figure by sampling their records, and they report the data shown in the following table. |Econo-Move |On-the-Move | |Total shipments sampled |900 |750 | |Number of shipments with a claim [pic] $50 |162 |60 | The owner of On-the-Move is hoping to use these data to show that the company is superior to Econo-Move with regard to the percentage of claims filed. Which test would be used to properly analyze the data in this experiment? a) test for independence b) test for goodness of fit ) ANOVA F test for main treatment effect d) test for the difference between proportions ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in two proportions 21. The Wall Street Journal recently ran an article indicating differences in the perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: â€Å"Do you think sexual harassment is a major problem in the American workplace? † Some 24% of the men, compared to 62% of the women, responded â€Å"Yes. Assuming W designates women’s responses and M designates men’s, what hypothesis should The Wall Street Journal test in order to show that its claim is true? a) H0: pW – pM [pic] 0 versus H1: pW – pM < 0 b) H0: pW – pM [pic] 0 versus H1: pW – pM > 0 c) H0: pW – pM = 0 versus H1: pW – pM [pic] 0 d) H0: (W – (M [pic] 0 versus H1: (W – (M > 0 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for difference in two proportions, form of hypothesis 22. The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women.The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: â€Å"Do you think sexual harassment is a major problem in the American workplace? † Some 24% of the men, compared to 62% of the women, responded â€Å"Yes. † Suppose that 150 women and 200 men were interviewed. For a 0. 01 level of significance, what is the critical value for the rejection region? a) 7. 173 b) 7. 106 c) 6. 635 d) 2. 33 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in two proportions, critical value 23.The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: â€Å"Do you think sexual harassment is a major problem in the American workplace? † Some 24% of the men, compared to 62% of the wome n, responded â€Å"Yes. † Suppose that 150 women and 200 men were interviewed. What is the value of the test statistic? a) 7. 173 b) 7. 106 c) 6. 635 d) 2. 33 ANSWER: a TYPE: MC DIFFICULTY: ModerateKEYWORDS: Z test for difference in two proportions, test statistic 24. The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: â€Å"Do you think sexual harassment is a major problem in the American workplace? † Some 24% of the men, compared to 62% of the women, responded â€Å"Yes. † Suppose that 150 women and 200 men were interviewed. What conclusion should be reached? a) Using a 0. 1 level of significance, there is sufficient evidence to conclude that women perceive the problem of sexual harassment on the job as being much more prevalent than do men. b) There is insufficient evidence to conclude with at least 99% confidence that women perceive the problem of sexual harassment on the job as being much more prevalent than do men. c) There is no evidence of a significant difference between the men and women in their perception. d) More information is needed to draw any conclusions from the data set. ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in two proportions, decision, conclusion 5. A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Which of the following are the appropriate null and alternative hypotheses to test the group’s claim? a) H0: pW – pM [pic] 0 versus H1: pW – pM < 0 b) H0: pW – pM [pic] 0 versus H1: pW – pM > 0 c) H0: pW – pM = 0 versus H1: pW – pM [pic] 0 ) H0: (W – (M [pic] 0 versus H1: (W – (M > 0 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in two proportions, form of hypothesis 26. A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Find the value of the test statistic. a) Z = – 2. 55 b) Z = – 0. 85 c) Z = – 1. 05 d) Z = – 1. 20ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in two proportions, test statistic 27. A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A gro up of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. If the p value turns out to be 0. 035 (which is NOT the real value in this data set), then a) at [pic] = 0. 05, we should fail to reject H0. ) at [pic] = 0. 04, we should reject H0. c) at [pic] = 0. 03, we should reject H0. d) None of the above would be correct statements. ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in two proportions, decision, conclusion TABLE 12-4 A few years ago, Pepsi invited consumers to take the â€Å"Pepsi Challenge. † Consumers were asked to decide which of two sodas, Coke or Pepsi, they preferred in a blind taste test. Pepsi was interested in determining what factors played a role in people’s taste preferences. One of the factors studied was the gender of the consumer.Below are the re sults of analyses comparing the taste preferences of men and women, with the proportions depicting preference for Pepsi. Males: n = 109, pSM = 0. 422018Females: n = 52, pSF = 0. 25 pSM – pSF = 0. 172018Z = 2. 11825 28. Referring to Table 12-4, to determine if a difference exists in the taste preferences of men and women, give the correct alternative hypothesis that Pepsi would test. a) H1: [pic] b) H1: [pic] c) H1: pM – pF [pic] 0 d) H1: pM – pF = 0 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for difference in two proportions, form of hypothesis 29.Referring to Table 12-4, suppose Pepsi wanted to test to determine if the males preferred Pepsi more than the females. Using the test statistic given, compute the appropriate p-value for the test. a) 0. 0171 b) 0. 0340 c) 0. 2119 d) 0. 4681 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in two proportions, p-value 30. Referring to Table 12-4, suppose Pepsi wanted to test to determine if the males preferred Pepsi less than the females. Using the test statistic given, compute the appropriate p-value for the test. a) 0. 0170 b) 0. 0340 c) 0. 9660 d) 0. 9830 ANSWER: d TYPE: MC DIFFICULTY: ModerateKEYWORDS: Z test for difference in two proportions, p-value 31. Referring to Table 12-4, suppose that the two-tailed p-value was really 0. 0734. State the proper conclusion. a) At [pic] = 0. 05, there is sufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi. b) At [pic] = 0. 10, there is sufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi. c) At [pic] = 0. 05, there is sufficient evidence to indicate the proportion of males preferring Pepsi equals the proportion of females preferring Pepsi. ) At [pic] = 0. 08, there is insufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of f emales preferring Pepsi. ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in two proportions, decision, conclusion TABLE 12-5 The following Excel output contains the results of a test to determine if the proportions of satisfied guests at two resorts are the same or different. |Hypothesized Difference |0 | |Level of Significance |0. 5 | |Group 1 | |Number of Successes |163 | |Sample Size |227 | |Group 2 | |Number of Successes |154 | |Sample Size |262 | |Group 1 Proportion |0. 18061674 | |Group 2 Proportion |0. 58778626 | |Difference in Two Proportions |0. 130275414 | |Average Proportion |0. 648261759 | |Test Statistic |3. 00875353 | |Two-Tailed Test | |Lower Critical Value |-1. 59961082 | |Upper Critical Value |1. 959961082 | |p-Value |0. 002623357 | 32. Referring to Table 12-5, allowing for 0. 75% probability of committing a Type I error, what are the decision and conclusion on testing whether there is any difference in the proportions of satisfied guest s in the two resorts? a.Do not reject the null hypothesis; there is enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts. b. Do not reject the null hypothesis; there is not enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts. c. Reject the null hypothesis; there is enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts. d.Reject the null hypothesis; there is not enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts. ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for difference in two proportions, decision, conclusion 33. Referring to Table 12-5, if you want to test the claim that â€Å"Resort 1 (Group 1) has a higher proportion of satisfied guests than Resort 2 (Group 2),† the p-value of the test will be a) 0. 00262. b) 0. 00262/2. c) 2*(0. 00262). d) 1-(0. 00262/2). ANSWER: bTYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in two proportions, p-value 34. Referring to Table 12-5, if you want to test the claim that â€Å"Resort 1 (Group 1) has a lower proportion of satisfied guests than Resort 2 (Group 2),† you will use a) a t test for the difference in two proportions. b) a Z test for the difference in two proportions. c) a [pic] test for the difference in two proportions. d) a [pic] test for independence. ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in two proportionsTABLE 12-6 One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. Since the job is repetitious, after the initial training period, any improvement due t o a learning effect might be offset by a loss of motivation. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table below. | |Years Since Training Period | | | |< 1 Year |1 – 4 Years |5 – 9 Years | | |High |6 |9 |9 | |Defect Rate: |Average |9 |19 |23 | | |Low |7 |8 |10 | 5. Referring to Table 12-6, which test would be used to properly analyze the data in this experiment to determine whether there is a relationship between defect rate and years of experience? a) [pic]test for independence in a two-way contingency table b) [pic]test for equal proportions in a one-way table c) ANOVA F test for main treatment effect d) Z test for the difference in two proportions ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: chi-square test of independence 36. Referring to Table 12-6, find the rejection region necessary for testing at the 0. 5 level of significance whether there is a relationship between defect rate and ye ars of experience. a) Reject H0 if [pic] > 16. 919. b) Reject H0 if [pic] > 15. 507. c) Reject H0 if [pic] > 11. 143. d) Reject H0 if [pic] > 9. 488. ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test of independence, critical value 37. Referring to Table 12-6, what is the expected number of employees with less than 1 year of training time and a high defect rate? a) 4. 17 b) 4. 60 c) 5. 28 d) 9. 17 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: chi-square test of independence, contingency table, properties 8. Referring to Table 12-6, what is the expected number of employees with 1 to 4 years of training time and a high defect rate? a) 12. 00 b) 8. 64 c) 6. 67 d) 6. 00 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: chi-square test of independence, contingency table, properties 39. Referring to Table 12-6, of the cell for 1 to 4 years of training time and a high defect rate, what is the contribution to the overall [pic] statistic for the independence test? a) 0. 36 b) 0. 1296 c) 0. 015 d) 0. 0144 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: chi-square test of independence, contingency table, properties 0. Referring to Table 12-6, a test was conducted to determine if a relationship exists between defect rate and years of experience. Which of the following p-values would indicate that defect rate and years of experience are dependent? Assume you are testing at [pic] = 0. 05. a) 0. 045 b) 0. 055 c) 0. 074 d) 0. 080 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test of independence, p-value, decision TABLE 12-7 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like to take such a course.The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted to take a self-improvement course. The groups are assumed to be independent random samples. Let p1 and p2 represent the true proportion of workers who would like to attend a self-impro vement course in the recent study and the past study, respectively. 41. Referring to Table 12-7, if the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses? a) H0: p1 – p2 = 0 versus H1: p1 – p2 [pic] 0 b) H0: p1 – p2 [pic] 0 versus H1: p1 – p2 = 0 ) H0: p1 – p2 [pic] 0 versus H1: p1 – p2 > 0 d) H0: p1 – p2 [pic] 0 versus H1: p1 – p2 < 0 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions, Z test for difference in two proportions 42. Referring to Table 12-7, if the firm wanted to test whether a greater proportion of workers would currently like to attend a self-improvement course than in the past, which represents the relevant hypotheses? a) H0: p1 – p2 = 0 versus H1: p1 – p2 [pic] 0 b) H0: p1 – p2 [pic] 0 versus H1: p1 – p2 = 0 c) H0: p1 – p2 [pic] 0 versus H1: p1 – p2 > 0 ) H0 : p1 – p2 [pic] 0 versus H1: p1 – p2 < 0 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for difference in two proportions, form of hypothesis 43. Referring to Table 12-7, what is the unbiased point estimate for the difference between the two population proportions? a) 0. 06 b) 0. 10 c) 0. 15 d) 0. 22 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: point estimate 44. Referring to Table 12-7, what is/are the critical value(s) when performing a Z test on whether population proportions are different if [pic] = 0. 05? a) [pic] 1. 645 b) [pic] 1. 96 c) -1. 96 d) [pic] 2. 8 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for difference in two proportions, critical value 45. Referring to Table 12-7, what is/are the critical value(s) when testing whether population proportions are different if [pic] = 0. 10? a) [pic] 1. 645 b) [pic] 1. 96 c) -1. 96 d) [pic] 2. 08 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for difference in two proportions, critical value 46. Referring to Table 12-7, what is/are the critical value(s) when testing whether the current population proportion is higher than before if [pic] = 0. 05? a) [pic]1. 645 b) + 1. 45 c) [pic]1. 96 d) + 1. 96 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions, critical value 47. Referring to Table 12-7, what is the estimated standard error of the difference between the two sample proportions? a) 0. 629 b) 0. 500 c) 0. 055 d) 0 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in two proportions, standard error 48. Referring to Table 12-7, what is the value of the test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions? ) 4. 335 b) 1. 96 c) 1. 093 d) 0 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in two proportions, chi-square test for difference in proportions, test statistic 49. Referring to Table 12-7, the company tests at the 0. 05 level to determine whether the population proportion has changed from the previous study. Which of the following is most correct? a) Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has changed over the intervening 10 years. ) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has not changed over the intervening 10 years. c) Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years. d) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years. ANSWER: b TYPE: MC DIFFICULTY: ModerateKEYWORDS: Z test for difference in two proportions, chi-square test for difference in proportions, decision, conclusion 50. True or Fal se: In testing the difference between two proportions, we may use either a one-tailed chi-square test or two-tailed Z test. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Z test for difference in two proportions, chi-square test for difference in proportions 51. True or False: The squared difference between the observed and theoretical frequencies should be large if there is no significant difference between the proportions.ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions, properties 52. True or False: A test for the difference between two proportions can be performed using the chi-square distribution. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions 53. True or False: A test for whether one proportion is higher than the other can be performed using the chi-square distribution. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions 54.True or False: When using the [pic] tests for independence, one should be aware that expected frequencies that are too small will lead to too big a Type I error. ANSWER: True TYPE: TF DIFFICULTY: Difficult KEYWORDS: chi-square test of independence, properties, assumption 55. True or False: If we use the chi-square method of analysis to test for the difference between proportions, we must assume that there are at least 5 observed frequencies in each cell of the contingency table. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: chi-square test of independence, properties, assumption 6. If we wish to determine whether there is evidence that the proportion of successes is higher in Group 1 than in Group 2, and the test statistic for Z = +2. 07, the p-value is equal to ______. ANSWER: 0. 0192 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Z test for difference in two proportions, p-value TABLE 12-8 The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors.In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as â€Å"Group 1† and the economics majors are designated as â€Å"Group 2,† perform the appropriate hypothesis test using a level of significance of 0. 05. 57. Referring to Table 12-8, the hypotheses the dean should use are: a) H0: p1 – p2 = 0 versus H1: p1 – p2 [pic] 0. b) H0: p1 – p2 [pic] 0 versus H1: p1 – p2 = 0. c) H0: p1 – p2 [pic] 0 versus H1: p1 – p2 > 0. d) H0: p1 – p2 [pic] 0 versus H1: p1 – p2 < 0.ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions, Z test for difference in two proportions, form of hypothesis 58. Referring to Table 12-8, the null hypot hesis will be rejected if the test statistic is ________. ANSWER: Z > 1. 96 or < -1. 96 or [pic] > 3. 841 TYPE: FI DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions, Z test for difference in two proportions, critical value 59. Referring to Table 12-8, the value of the test statistic is ________. ANSWER: Z = 1. 866 or [pic] = 3. 4806 TYPE: FI DIFFICULTY: ModerateKEYWORDS: chi-square test for difference in proportions, Z test for difference in two proportions, test statistic 60. Referring to Table 12-8, the p-value of the test is ________. ANSWER: 0. 0621 TYPE: FI DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, Z test for difference in two proportions, p-value 61. True or False: Referring to Table 12-8, the null hypothesis should be rejected. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions, Z test for difference in two proportions, decision 62.True or False: Referring to Table 12-8, th e same decision would be made with this test if the level of significance had been 0. 01 rather than 0. 05. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, Z test for difference in two proportions, decision 63. True or False: Referring to Table 12-8, the same decision would be made with this test if the level of significance had been 0. 10 rather than 0. 05. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, Z test for difference in two proportions, decision TABLE 12-9A quality control engineer is in charge of the manufacture of computer disks. Two different processes can be used to manufacture the disks. He suspects that the Kohler method produces a greater proportion of defects than the Russell method. He samples 150 of the Kohler and 200 of the Russell disks and finds that 27 and 18 of them, respectively, are defective. If Kohler is designated as â€Å"Group 1† and Russell is designated as â€Å"Group 2,† perform the appropriate test at a level of significance of 0. 01. 64. Referring to Table 12-9, the hypotheses that should be tested are: a) H0: p1 – p2 = 0 versus H1: p1 – p2 [pic] 0. ) H0: p1 – p2 [pic] 0 versus H1: p1 – p2 = 0. c) H0: p1 – p2 [pic] 0 versus H1: p1 – p2 > 0. d) H0: p1 – p2 [pic] 0 versus H1: p1 – p2 < 0. ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for difference in two proportions, form of hypothesis 65. Referring to Table 12-9, the null hypothesis will be rejected if the test statistic is ________. ANSWER: Z > 2. 33 TYPE: FI DIFFICULTY: Easy KEYWORDS: Z test for difference in two proportions, critical value 66. Referring to Table 12-9, the value of the test statistic is ________. ANSWER: 2. 49 TYPE: FI DIFFICULTY: ModerateKEYWORDS: Z test for difference in two proportions, test statistic 67. Referring to Table 12-9, the p-value of the test is ________. ANSWER: 0. 0064 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Z test for difference in two proportions, p-value 68. True or False: Referring to Table 12-9, the null hypothesis should be rejected. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Z test for difference in two proportions, decision 69. True or False: Referring to Table 12-9, the same decision would be made with this test if the level of significance had been 0. 05 rather than 0. 01. ANSWER: True TYPE: TF DIFFICULTY: ModerateKEYWORDS: Z test for difference in two proportions, decision 70. True or False: Referring to Table 12-9, the same decision would be made if this had been a two-tailed test at a level of significance of 0. 01. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Z test for difference in two proportions, decision TABLE 12-10 The director of transportation of a large company is interested in the usage of her van pool. She considers her routes to be divided into local and non-local. She is particularly intereste d in learning if there is a difference in the proportion of males and females who use the local routes.She takes a sample of a day's riders and finds the following: | |Male |Female |Total | |Local |27 |44 |71 | |Non-Local |33 |25 |58 | |Total |60 |69 |129 | She will use this information to perform a chi-square hypothesis test using a level of significance of 0. 05. 71. Referring to Table 12-10, the test will involve _________ degree(s) of freedom. ANSWER: 1TYPE: FI DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions, degrees of freedom 72. Referring to Table 12-10, the overall or average proportion of local riders is __________. ANSWER: 0. 550 TYPE: FI DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions, properties 73. Referring to Table 12-10, the expected cell frequency in the Male/Local cell is __________. ANSWER: 33. 02 TYPE: FI DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, contingency table, properties 74 . Referring to Table 12-10, the expected cell frequency in the Female/Non-Local cell is __________.ANSWER: 31. 02 TYPE: FI DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, contingency table, properties 75. Referring to Table 12-10, the critical value of the test is _________. ANSWER: 3. 841 TYPE: FI DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions, critical value 76. Referring to Table 12-10, the value of the test statistic is _________. ANSWER: 4. 568 TYPE: FI DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, test statistic 77. True or False: Referring to Table 12-10, the null hypothesis will be rejected.ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, decision 78. True or False: Referring to Table 12-10, the decision made suggests that there is a difference between the proportion of males and females who ride local versus non-local routes. ANSWER: Tru e TYPE: TF DIFFICULTY: Median KEYWORDS: chi-square test for difference in proportions, conclusion TABLE 12-11 Four surgical procedures are currently used to install pacemakers. If the patient does not need to return for follow-up surgery, the operation is called a â€Å"clear† operation.A heart center wants to compare the proportion of clear operations for the 4 procedures, and collects the following numbers of patients from their own records: | |Procedure | | | |A |B |C |D |Total | |Clear |27 |41 |21 |7 |96 | |Return |11 |15 |9 |11 |46 | |Total |38 |56 |30 |18 |142 They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0. 05. 79. Referring to Table 12-11, the test will involve _________ degrees of freedom. ANSWER: 3 TYPE: FI DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions, degrees of freedom 80. Referring to Table 12-11, the overall or average proportion of clear operations is __________. ANSWER: 0. 676 TYPE: FI DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions, properties 81.Referring to Table 12-11, the expected cell frequency for the Procedure A/Clear cell is __________. ANSWER: 25. 69 TYPE: FI DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, contingency table, properties 82. Referring to Table 12-11, the expected cell frequency for the Procedure D/Return cell is __________. ANSWER: 5. 83 TYPE: FI DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, contingency table, properties 83. Referring to Table 12-11, the critical value of the test is ________. ANSWER: 7. 815 TYPE: FI DIFFICULTY: EasyKEYWORDS: chi-square test for difference in proportions, critical value 84. Referring to Table 12-11, the value of the test statistic is _________. ANSWER: 7. 867 TYPE: FI DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, test statistic 85 . True or False: Referring to Table 12-11, the null hypothesis will be rejected. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, decision 86. True or False: Referring to Table 12-11, the decision made suggests that the 4 procedures all have different proportions of clear operations.ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, conclusion 87. True or False: Referring to Table 12-11, the decision made suggests that the 4 procedures do not all have the same proportion of clear operations. 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ANSWER: 13. 277 TYPE: FI DIFFICULTY: Easy KEYWORDS: chi-square test of independence, critical value 90. Referring to Table 12-12, the expected cell frequency for the Admitted/Urban cell is _________. ANSWER: 39. 06TYPE: FI DIFFICULTY: Moderate KEYWORDS: chi-square test of independence, contingency table, properties 91. Referring to Table 12-12, the value of the test statistic is _________. ANSWER: 12. 624 TYPE: FI DIFFICULTY: Moderate KEYWORDS: chi-square test of indep endence, test statistic 92. True or False: Referring to Table 12-12, the null hypothesis will be rejected. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: chi-square test of independence, decision 93. True or False: Referring to Table 12-12, the p-value of this test is greater than 0. 01. ANSWER: TrueTYPE: TF DIFFICULTY: Moderate KEYWORDS: chi-square test of independence, p-value 94. True or False: Referring to Table 12-12, the decision made suggests that admissions status at the college is independent of the type of community in which an applicant resides. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: chi-square test of independence, conclusion 95. True or False: Referring to Table 12-12, the same decision would be made with this test if the level of significance had been 0. 005. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: chi-square test of independence, decision 6. True or False: Referring to Table 12-12, the same decision would be made with this test if the level o f significance had been 0. 05. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: chi-square test of independence, decision 97. True or False: Referring to Table 12-12, the null hypothesis claims that â€Å"there is no association between admission status at the college and the type of community in which an applicant resides. † ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: chi-square test of independence, form of hypothesis, conclusion 98.True or False: Referring to Table 12-12, the alternative hypothesis claims that â€Å"there is some connection between admission status at the college and the type of community in which an applicant resides. † ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: chi-square test of independence, form of hypothesis, conclusion 99. True or False: The chi-square test of independence requires that the number of expected frequency in each cell to be at least 5. ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: chi-square test of independence, assumption 100.True or False: The chi-square test of independence requires that the number of expected frequency in each cell to be at least 1. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: chi-square test of independence, assumption TABLE 12-13 Parents complain that children read too few story books and watch too much television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading story books: | |Average time spent reading story books | |Average time pent watching TV |Less than 1 hour |Between 1 and 2 hours |More than 2 hours | |Less than 2 hours |90 |85 |130 | |More than 2 hours |655 |32 |8 | 101. Referring to Table 12-13, how many children in the survey spent less than 2 hours watching TV and more than 2 hours reading story books, on average? a) 8 b) 130 c) 175 d) 687 ANSWER: bTYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, properties 102. Referring to Table 12-13, how many children in the survey spent less than 2 hours watching TV and no more than 2 hours reading story books, on average? a) 8 b) 130 c) 175 d) 687 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, properties 103. Referring to Table 12-13, if the null hypothesis of no connection between time spent watching TV and time spent reading story books is true, how many children watching less than 2 hours of TV and reading no more than 2 hours of story books, on average, can we expect? ) 35. 69 b) 227. 23 c) 262. 91 d) 969. 75 ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: chi-square test of independence, contingency table, properties 104. Referring to Table 12-13, if the null hypothesis of no connection between time spent watching TV and time spent reading story books is true, how many children watching less than 2 hours of TV and reading more than 2 hours of story books, on average, can we expect? a) 42. 09 b) 155. 25 c) 262. 92 d) 987. 75 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS : chi-square test of independence, contingency table, properties 105.Referring to Table 12-13, to test whether there is any relationship between average time spent watching TV and average time spent reading story books, the value of the measured test statistic is a) -12. 59. b) 1. 61. c) 481. 49. d) 1,368. 06. ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: chi-square test of independence, test statistic 106. Referring to Table 12-13, suppose we want to constrain the probability of committing a Type I error to 5% when testing whether there is any relationship between average time spent watching TV and average time spent reading story books.The critical value will be a) 5. 991. b) 7. 378. c) 12. 592. d) 14. 449. ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test of independence, critical value 107. Referring to Table 12-13, we want to test whether there is any relationship between average time spent watching TV and average time spent reading story books. Suppose the valu e of the test statistic was 164 (which is not the correct answer) and the critical value was 19. 00 (which is not the correct answer), then we could conclude that a) there is a connection between time spent reading story books and time spent watching TV. ) there is no connection between time spent reading story books and time spent watching TV. c) more time spent reading story books leads to less time spent watching TV. d) more time spent watching TV leads to less time spent reading story books. ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: chi-square test of independence, decision, conclusion TABLE 12-14 Recent studies have found that American children are more obese than in the past. The amount of time children spend watching television has received much of the blame.A survey of 100 ten-year-olds revealed the following with regards to weights and average number of hours a day spent watching television. We are interested in testing whether the average number of hours spent watc hing TV and weights are independent at 1% level of significance. |Weights |TV Hours |Total | | |0-3 |3-6 |6+ | | |More than 10 lbs. verweight |1 |9 |20 |30 | |Within 10 lbs. of normal weight |20 |15 |15 |50 | |More than 10 lbs. underweight |10 |5 |5 |20 | |Total |31 |29 |40 |100 | 108.Referring to Table 12-14, if there is no connection between weights and average number of hours spent watching TV, we should expect how many children to be spending 3-6 hours, on average, watching TV and are more than 10 lbs. underweight? a) 5 b) 5. 8 c) 6. 2 d) 8 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test of independence, contingency table, properties 109. Referring to Table 12-14, if there is no connection between weights and average number of hours spent watching TV, we should expect how many children to be spending no more than 6 hours, on average, watching TV and are more than 10 lbs. nderweight? a) 5. 8 b) 6. 2 c) 8 d) 12 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: chi- square test of independence, contingency table, properties 110. Referring to Table 12-14, how many children in the survey spend more than 6 hours watching TV and are more than 10 lbs. overweight? a) 1 b) 9 c) 20 d) 40 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test of independence, contingency table, properties 111. Referring to Table 12-14, how many children in the survey spend no more than 6 hours watching TV and are more than 10 lbs. underweight? a) 5 ) 10 c) 15 d) 20 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test of independence, contingency table, properties 112. Referring to Table 12-14, the value of the test statistic is a) 8. 532. b) 15. 483. c) 18. 889. d) 69. 744. ANSWER: c TYPE: MC DIFFICULTY: moderate KEYWORDS: chi-square test of independence, test statistic 113. Referring to Table 12-14, the critical value of the test will be a) 6. 635. b) 13. 277. c) 14. 860. d) 21. 666. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test of indep endence, critical value 114.Referring to Table 12-14, suppose the value of the test statistic was 30. 00 (which is not the correct value) and the critical value at 1% level of significance was 10. 00 (which is not the correct value), which of the following conclusions would be correct? a) We will accept the null and conclude that the average number of hours spent watching TV and weights are independent. b) We will reject the null and conclude that the average number of hours spent watching TV and weights are independent. c) We will accept the null and conclude that the average number of hours spent watching TV and weights are not independent. ) We will reject the null and conclude that the average number of hours spent watching TV and weights are not independent. ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: chi-square test of independence, decision, conclusion 115. Referring to Table 12-14, which of the following statements is correct? a) We can accept the null for any level of significance greater than 0. 005 b) We can reject the null for any level of significance greater than 0. 005. c) We can accept the null for any level of significance smaller than 0. 005 d) We can reject the null for any level of significance smaller than 0. 05. ANSWER: b TYPE: MC DIFFICULTY: Difficult KEYWORDS: chi-square test of independence, decision 116. Referring to Table 12-14, the degrees of freedom of the test statistic are a) 1. b) 2. c) 4. d) 9. ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test of independence, degrees of freedom 117. True or False: Referring to Table 12-14, the test is always a one-tailed test. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: chi-square test of independence, properties Table 12-15 According to an article in Marketing News, fewer checks are being written at grocery store checkout stands than in the past.To determine whether there is a difference in the proportion of shoppers who paid by check over three consecutive years at a 0 . 05 level of significance, the results of a survey of 500 shoppers during three consecutive years are obtained and presented below. | |Year | |Check Written |Year 1 |Year 2 |Year 3 | |Yes |225 |175 |125 | |No |275 |325 |375 | 118.Referring to Table 12-15, what is the expected number of shoppers who paid by check in year 1 if there was no difference in the proportion of shoppers who paid by check over the three years? ANSWER: 175 TYPE: PR DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions, properties 119. Referring to Table 12-15, what is the expected number of shoppers who did not pay by check in year 3 if there was no difference in the proportion of shoppers who paid by check over the three years? ANSWER: 325 TYPE: PR DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions, properties 20. Referring to Table 12-15, what is the form of the null hypothesis? a) [pic] b) [pic] c) [pic] d) [pic] ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-squ are test for difference in proportions, forms of hypothesis 121. Referring to Table 12-15, what is the form of the alternative hypothesis? a) [pic] b) [pic] c) [pic] d) [pic] not all [pic] are the same ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions, forms of hypothesis 122. True or False: Referring to Table 12-15, the assumptions needed to perform the test are satisfied. ANSWER:True TYPE: TF DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, assumption 123. Referring to Table 12-15, what are the degrees of freedom of the test statistic? ANSWER: 2 TYPE: PR DIFFICULTY: Easy KEYWORDS: chi-square test for difference in proportions, degrees of freedom 124. Referring to Table 12-15, what is the value of the test statistic? ANSWER: 43. 96 TYPE: PR DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, test statistic 125. Referring to Table 12-15, what is the critical value? ANSWER: 5. 99 TYPE: PR DIFFICULTY: EasyKEYWORDS: chi-square test for difference in proportions, critical value 126. Referring to Table 12-15, what is the p-value of the test statistic? ANSWER: 2. 9E-10 or smaller than 0. 005 TYPE: PR DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, p-value 127. True or False: Referring to Table 12-15, the null hypothesis cannot be rejected. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, decision 128. Referring to Table 12-15, what is the correct conclusion? a) There is enough evidence that the proportions are all different in the 3 years. ) There is not enough evidence that the proportions are all different in the 3 years. c) There is enough evidence that at least two of the proportions are not equal. d) There is not enough evidence that at least two of the proportions are not equal. ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, conclusion 129. Referring to Table 12-15, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between year 1 and year 2 using a 0. 05 level of significance? ANSWER: 0. 0754 TYPE: PR DIFFICULTY: DifficultKEYWORDS: chi-square test for difference in proportions, Marascuilo procedure, critical value 130. 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ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, Marascuilo procedure, decision, conclusion 133.True or False: Referring to Table 12-15, there is not sufficient evidence to conclude that the proportions between year 1 and year 3 are different at a 0. 05 level of significance. ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, Marascuilo procedure, decision, conclusion 134. True or False: Referring to Table 12-15, there is sufficient evidence to conclude that the proportions between year 2 and year 3 are different at a 0. 05 level of significance. ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: chi-square test for difference in proportions, Marascuilo procedure, decision conclusion

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Chapter 13 - Assignment Example They came to the United States two years ago. In India, people react to strangers in different ways. Some Indians simply look at strangers, others smile, while others pretend to not care, but they surely notice foreigners around them (Bhatti). If someone is staring, the stranger can smile politely. Indians often return the smile (Bhatti). In terms of greeting, saying â€Å"Namaste† is the traditional greeting (â€Å"India Customs†). During this greeting, the person presses his/her hands together, with his/her fingers facing up and near the chin (â€Å"India Customs†). When addressing superiors or older people, a slight bow is added (â€Å"India Customs†). One must greet the most senior person or the eldest first always (â€Å"India Customs†). When entering a room, a nod and saying â€Å"Namaste† can suffice (â€Å"India Customs†). Males, especially strangers, do not touch women in public, including shaking their hands (â€Å"India Customs†). For communication practices, excessive gestures and verbal expression are considered impolite, especially when coming from strangers (Dasgupta). It is also acceptable to be late by 15 to 30 minutes because American punctuality is not widely practiced in many areas, unless for businesses who have embraced American customs (Dasgupta). In addition, when invited to an Indian family house for lunch or dinner, the invited person must bring a gift, such as a box of chocolates or flowers (Dasgupta). However, since different flowers have different meanings, it is important to ask the florist about appropriate flowers to be brought to families (Dasgupta). Furthermore, the gesture for â€Å"yes† is a slight nod of the head, while â€Å"no† is a turning from side to side. Some foreigners do not easily see the difference between the gestures for â€Å"yes† and â€Å"no,† probably because Indians do not like saying â€Å"no† out of respect (Dasgupta). Greeting a person depends on his/her social status, wherein age, university

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Regression Analysis Questions Assignment Example | Topics and Well Written Essays - 250 words

Regression Analysis Questions - Assignment Example The explanatory variable is the scale upon which the dependent or the response variable changes, for instance time. The constant represent the unwavering value in the regression equation, for instance, fixed costs. An example of a multiple regression would be = mX + nZ, which is an equation to calculate profit for a company. The variable Y would be for profit margin, X for fixed costs and Z for variable costs. The values of m and n are the coefficients of X and Z respectively. The value of m would tell of the rate of change in slope attributable to X while n would show the rate of change of slope attributable to Z. By assuming that the impacts of the other two components, which make 20% of the total sales are negligible, the error value increases significantly. In addition, since items B and C form part of the error, and will change with varying values of A, the model with be heteroscedastic, hence more difficult to use for the underlying trend in the data. Consequently, a linear model would make a poor fit for the data. Therefore, this use of regression analysis would be