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Questions and Answers of Statistics

Corporate women are still struggling to break into senior management ranks, according to a study of senior corporate executives by Korn/Ferry International, New York recruiter. Of 1,362 top
According to The Economist, the current office vacancy rate in San Jose, California, is 21%.An economist knows that this British publication likes to disparage America and suspects that The Economist
At Armco's steel plant in Middletown, Ohio, statistical quality-control methods have been used very successfully in controlling slab width on continuous casting units. The company claims that a large
According to the mortgage banking firm Lomas & Nettleton, 95% of all households in the second half of last year lived in rental accommodations. The company believes that lower interest rates for
A recent study was aimed at determining whether people with increased workers' compensation stayed off the job longer than people without the increased benefits. Suppose that the average time off per
Environmental changes have recently been shown to improve firms' competitive advantages. The approach is called the multiple-scenario approach. A study was designed to find the percentage of the
According to an article in the New York Times, new Internet dating Web sites use sex to advertise their services. One such site, True.com, reportedly received an average of 3.8 million visitors per
Executives at Gammon & Ninowski Media Investments, a top television station brokerage, believe that the current average price for an independent television station in the United States is $125
Microsoft Corporation makes software packages for use in microcomputers. The company believes that if at least 25% of present owners of microcomputers of certain types would be interested in a
A recent National Science Foundation (NSF) survey indicates that more than 20% of the staff in U.S. research and development laboratories are foreign-born. Results of the study have been used for
The average number of weeks that banner ads run at a Web site is estimated to be 5.5. You want to check the accuracy of this estimate. A sample of 50 ads reveals a sample average of 5.1 weeks with a
According to The New York Times, 3-D printers are now becoming a reality. If a manufacturer of the new high-tech printers claims that the new device can print a page in 3 seconds on average, and a
Out of all the air-travel bookings in major airlines, at least 58% are said to be done online. A sample of 70 airlines revealed that 52% of bookings for last year were done online. State the null and
According to The Economist, investors in Porsche are the dominant group within the larger VW Company that now owns the sports car maker. Let's take dominance to mean 50% ownership, and suppose that a
Suppose that a claim is made that the average billionaire is 60 years old or younger. The following is a random sample of billionaires' ages, drawn from the Forbes list.80, 70, 76, 54, 59, 52, 74,
An article in BusinessWeek says: "Today companies use a mere 40% of their space."19 Suppose you want to disprove this claim, suspecting that it is an upward exaggeration. A random sample of the
The best places in the United States to be a job seeker are state capitals and university towns, which are claimed to have jobless rates below the national average of 4.2%. A sample of 50 towns and
Consider the null hypothesis μ ≥ 56. The population standard deviation is guessed to be 2.16. Type II error probabilities are to be calculated at μ = 55.a. Draw a β versus α chart with sample
The null hypothesis p = 0.25 is tested with n = 1,000 and α = 5%.a. Draw the power curve. What is the power when p = 0.22?b. Draw the OC curve for n = 1,000 and 1,200. Is there a lot to gain by
The null hypothesis μ ≤ 30 is to be tested. The population standard deviation is guessed to be 0.52. Type II error probabilities are to be calculated at μ = 30.3.a. Draw a β versus α chart with
If you look at the power curve or the OC curve of a two-tailed test, you see that there is no region that represents instances of type I error, whereas there are large regions that represent
The average weight of airline food packaging material is to be controlled so that the total weight of catering supplies does not exceed desired limits. An inspector who uses random sampling to accept
A market research study is undertaken to test which of two popular electric shavers, a model made by Norelco or a model made by Remington, is preferred by consumers. A random sample of 25 men who
The photography department of a fashion magazine needs to choose a camera. Of the two models the department is considering, one is made by Nikon and one by Minolta. The department contracts with an
Marcus Robert Real Estate Company wants to test whether the average sale price of residential properties in a certain size range in Bel Air, California, is approximately equal to the average sale
Fortune compared global equities versus investments in the U.S. market. For the global market, the magazine found an average of 15% return over five years, while for U.S. markets it found an average
Many companies that cater to teenagers have learned that young people respond to commercials that provide dance-beat music, adventure, and a fast pace rather than words. In one test, a group of 128
New corporate strategies take years to develop. Two methods for facilitating the development of new strategies by executive strategy meetings are to be compared.One method is to hold a two-day
A fashion industry analyst wants to prove that models featuring Liz Claiborne clothing earn on average more than models featuring clothes designed by Calvin Klein. For a given period of time, a
Active Trader compared earnings on stock investments when companies made strong pre-earnings announcements versus cases where pre-earnings announcements were weak. Both sample sizes were 28. The
A brokerage firm is said to provide both brokerage services and "research" if, in addition to buying and selling securities for its clients, the firm furnishes clients with advice about the value of
The recent boom in sales of travel books has led to the marketing of other travel-related guides, such as video travel guides and audio walking-tour tapes. Waldenbooks has been studying the market
Business schools at certain prestigious universities offer nondegree management training programs for high-level executives. These programs supposedly develop executives' leadership abilities and
The performance ratings of two sports cars, the Mazda RX7 and the Nissan 300ZX, are to be compared. A random sample of 40 drivers is selected to drive the two models. Each driver tries one car of
Recent low-fare flights between Britain and eastern European destinations have brought large groups of English partygoers to cities such as Prague and Budapest.According to the New York Times, cheap
As the U.S. economy cools down, investors look to emerging markets to offer growth opportunities. In China, investments have continued to grow. Suppose that a random sample of 15 investments in U.S.
Ikarus, the Hungarian bus maker, lost its important Commonwealth of Independent States market and is reported on the verge of collapse. The company is now trying a new engine in its buses and has
Air Transport World recently named the Dutch airline KLM "Airline of the Year." One measure of the airline's excellent management is its research effort in developing new routes and improving service
According to Money, the average yield of a 6-month bank certificate of deposit (CD) is 3.56%, and the average yield for money market funds (MMFs) is 4.84%. Assume that these two averages come from
Mark Pollard, financial consultant for Merrill Lynch, Pierce, Fenner & Smith, Inc., is quoted in national advertisements for Merrill Lynch as saying: "I've made more money for clients by saying
An article reports the results of an analysis of stock market returns before and after antitrust trials that resulted in the breakup of AT&T. The study concentrated on two periods: the
The cosmetics giant Avon Products recently hired a new advertising firm to promote its products. Suppose that following the airing of a random set of 8 commercials made by the new firm, company sales
In problem 8-25, construct a 95% confidence interval for the difference between the average return to investors following a no recommendation and the average return to investors following a yes
Airline mergers cause many problems for the airline industry. One variable often quoted as a measure of an airline's efficiency is the percentage of on-time departures. Following the merger of
Recent advances in cell phone screen quality have enabled the showing of movies and commercials on cell phone screens. But according to the New York Times, advertising is not as successful as movie
A physicians' group is interested in testing to determine whether more people in small towns choose a physician by word of mouth in comparison with people in large metropolitan areas. A random sample
A corporate raider has been successful in 11 of 31 takeover attempts. Another corporate raider has been successful in 19 of 50 takeover bids. Assuming that the success rate of each raider at each
A random sample of 2,060 consumers shows that 13% prefer California wines. Over the next three months, an advertising campaign is undertaken to show that California wines receive awards and win taste
In problem 8-32, give a 95% confidence interval for the increase in the population proportion of consumers preferring California wines following the campaign. In problem A random sample of 2,060
Federal Reserve Board regulations permit banks to offer their clients commercial paper. A random sample of 650 customers of Bank of America reveals that 48 own commercial paper as part of their
Airbus Industrie, the European maker of the A380 long-range jet, is currently trying to expand its market worldwide. At one point, Airbus managers wanted to test whether their potential market in the
Data from the Bureau of Labor Statistics indicate that in one recent year the unemployment rate in Cleveland was 7.5% and the unemployment rate in Chicago was 7.2%. Suppose that both figures are
Recently, Venezuela instituted a new accounting method for its oil revenues. Suppose that a random sample of 100 accounting transactions using the old method reveals 6 errors. Is there evidence of
According to USA Today, 32% of the public think that credit cards are safer than debit cards, while 19% believe that debit cards are safer than credit cards. If these results are based on two
Several companies have been developing electronic guidance systems for cars. Motorola and Germany's Blaupunkt are two firms in the forefront of such research. Out of 120 trials of the Motorola model,
A study is undertaken to determine how consumers react to energy conservation efforts. A random group of 60 families is chosen. Their consumption of electricity is monitored in a period before and a
Compaq Computer Corporation has an assembly plant in Houston, where the company's Deskpro computer is built. Engineers at the plant are considering a new production facility and are interested in
Test the validity of the equal-variance assumption in problem 8-27.In problem The cosmetics giant Avon Products recently hired a new advertising firm to promote its products. Suppose that following
Test the validity of the equal-variance assumption for the data presented in problem 8-25.In problem Mark Pollard, financial consultant for Merrill Lynch, Pierce, Fenner & Smith, Inc., is quoted
Test the validity of the equal-variance assumption for the data presented in problem 8–26.In problem An article reports the results of an analysis of stock market returns before and after antitrust
The following data are independent random samples of sales of the Nissan Pulsar model made in a joint venture of Nissan and Alfa Romeo. The data represent sales at dealerships before and after the
A large department store wants to test whether the variance of waiting time in two checkout counters is approximately equal. Two independent random samples of 25 waiting times in each of the counters
An important measure of the risk associated with a stock is the standard deviation, or variance, of the stock's price movements. A financial analyst wants to test the one-tailed hypothesis that stock
According to Money, the average cost of repairing a broken leg is $10,402, and the average cost of repairing a knee injury is $11,359.12 Assume that these two statistics are sample averages based on
In problem 8-48, construct a 99% confidence interval for the difference between the average cost of repairing a broken leg and the average cost of repairing an injured knee. Interpret your results.In
A nationwide retailer wants to test whether new product shelf facings are effective in increasing sales volume. New shelf facings for the soft drink Country Time are tested at a random sample of 15
"Strategizing for the future" is management lingo for sessions that help managers make better decisions. Managers who deliver the best stock performance get results by bold, rule-breaking strategies.
For problem 8-50, construct a 95% confidence interval for the difference in stock performance.In problem "Strategizing for the future" is management lingo for sessions that help managers make better
According to a study reported in the New York Times, 48% of the viewers who watched NFL Football on TiVo viewed 1 to 6 commercials, while 26% of the viewers who watched Survivor: Cook Islands on TiVo
For problem 8-52, give a 99% confidence interval for the difference between the proportions for viewers of the two shows who watched 1 to 6 commercials. Interpret the results.In problem According to
According to the New York Times, the average number of roses imported to the United States from Costa Rica is 1,242 per month, while the average number imported from Guatemala each month is 1,240.14
Two movies were screen-tested at two different samples of theaters. Mystic River was viewed at 80 theaters and was considered a success in terms of box office sales in 60 of these theaters. Swimming
For problem 8-55, give a 95% confidence interval for the difference in proportion of theaters nationwide where one movie will be preferred over the other. Is the point 0 contained in the interval?
Two 12-meter boats, the K boat and the L boat, are tested as possible contenders in the America's Cup races. The following data represent the time, in minutes, to complete a particular track in
In problem 8-57, assume that the data points are paired as listed and that each pair represents performance of the two boats at a single trial. Conduct the test, using this assumption. What is the
Home loan delinquencies have recently been causing problems throughout the American economy. According to USA Today, the percentage of homeowners falling behind on their mortgage payments in some
Travel & Leisure conducted a survey of affordable hotels in various European countries.2 The following list shows the prices (in U.S. dollars) for one night of a double hotel room at comparable
The IIT Technical Institute claims "94% of our graduates get jobs." Assume that the result is based on a random sample of 100 graduates of the program. Suppose that an independent random sample of
The power of supercomputers derives from the idea of parallel processing. Engineers at Cray Research are interested in determining whether one of two parallel processing designs produces faster
Test the validity of the equal-variance assumption in problem 8-61. If you reject the null hypothesis of equal-population variance, redo the test of problem 8-61 using another method.In problem The
The senior vice president for marketing at Westin Hotels believes that the company's recent advertising of the Westin Plaza in New York has increased the average occupancy rate at that hotel by at
For problem 8-63, test the validity of the equal-variance assumption.In problem The senior vice president for marketing at Westin Hotels believes that the company's recent advertising of the Westin
Refer to problem 8-48. Test the null hypothesis that the variance of the cost of repairing a broken leg is equal to the variance of the cost of repairing an injured knee.In problem According to
Refer to problem 8-57. Do you believe that the variance of performance times for the K boat is about the same as the variance of performance times for the L boat? Explain. What are the implications
A company is interested in offering its employees one of two employee benefit packages. A random sample of the company's employees is collected, and each person in the sample is asked to rate each of
A company that makes electronic devices for use in hospitals needs to decide on one of two possible suppliers for a certain component to be used in the devices. The company gathers a random sample of
Refer to problem 8-68. Give a 95% confidence interval for the difference in the proportions of defective items made by suppliers A and B.In problem, A company that makes electronic devices for use in
In problem 8–4, suppose that the population standard deviation is 1.0 and that the true average reduction in consumption for the entire population in the area is μD = 0.1. For a sample size of 60
Refer to problem 8-63. Give a 90% confidence interval for the difference in average occupancy rates at the Westin Plaza hotel before and after the advertising.In problem The senior vice president for
Toys are entering the virtual world, and Mattel recently developed a digital version of its famous Barbie. The average price of the virtual doll is reported to be $60.16 A competing product sells for
Microlenders are institutions that lend relatively small amounts of money to businesses. An article on microlenders compared the average return on equity for lenders of two categories based on their
Refer to the situation of problem 8-72. The study also compared average portfolios of microloans. For the Alpha group it was $50 million, and for the Beta group it was $14 million. Assume the Alpha
According to Labor Department statistics, the average U.S. work week shortened from 39 hours in the 1950s and early 1960s to 35 hours in the 1990s. Assume the two statistics are based on independent
According to Fortune, there has been an average decrease of 86% in the Atlantic cod catch over the last two decades. Suppose that two areas are monitored for catch sizes and one of them has a daily
A survey finds that 62% of lower-income households have Internet access at home as compared to 70% of upper-income households. Assume that the data are based on random samples of size 500 each. Does
For problem 8-75, construct a 95% confidence interval for the difference between average catch in the two locations.In problem According to Fortune, there has been an average decrease of 86% in the
Two statisticians independently estimate the variance of the same normally distributed population, each using a random sample of size 10. One of their estimates is 3.18 times as large as the other.
A manufacturer uses two different trucking companies to ship its merchandise. The manufacturer suspects that one company is charging more than the other and wants to test it. A random sample of the
Consider the information in the following table.Assume that the television programs were randomly selected from the population of all prime-time TV programs. Also assume that ratings are normally
Ethanol is getting wider use as car fuel when mixed with gasoline.3 A car manufacturer wants to evaluate the performance of engines using ethanol mix with that of pure gasoline. The sample average

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