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essentials of statistics
Essentials Of Statistics For Business And Economics 5th Edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams - Solutions
16. Reis, Inc., a New York real estate research firm, tracks the cost of apartment rentals in the United States. In mid-2002, the nationwide mean apartment rental rate was $895 per month(The Wall Street Journal, July 8, 2002). Assume that, based on the historical quarterly surveys, a population
15. Individuals filing federal income tax returns prior to March 31 received an average refund of $1056. Consider the population of “last-minute” filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15).a. A researcher suggests that a
14. Consider the following hypothesis test:H0:Ha:μ 22μ 22 A sample of 75 is used and the population standard deviation is 10. Compute the p-value and state your conclusion for each of the following sample results. Use α .01.a. 23b. 25.1c. 20
13. Consider the following hypothesis test:A sample of 60 is used and the population standard deviation is 8. Use the critical value approach to state your conclusion for each of the following sample results. Useα .05.a. 52.5b. 51c. 51.8
12. Consider the following hypothesis test:A sample of 100 is used and the population standard deviation is 12. Compute the p-value and state your conclusion for each of the following sample results. Use α .01.a. 78.5b. 77c. 75.5d. 81
11. Consider the following hypothesis test:A sample of 50 provided a sample mean of 14.15. The population standard deviation is 3.a. Compute the value of the test statistic.b. What is the p-value?c. At α .05, what is your conclusion?d. What is the rejection rule using the critical value? What is
10. Consider the following hypothesis test:A sample of 40 provided a sample mean of 26.4. The population standard deviation is 6.a. Compute the value of the test statistic.b. What is the p-value?c. At α .01, what is your conclusion?d. What is the rejection rule using the critical value? What is
9. Consider the following hypothesis test:H0:Ha:μ 20μ 20 A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.a. Compute the value of the test statistic.b. What is the p-value?c. Using α .05, what is your conclusion?d. What is the rejection rule using the
8. Suppose a new production method will be implemented if a hypothesis test supports the conclusion that the new method reduces the mean operating cost per hour.a. State the appropriate null and alternative hypotheses if the mean cost for the current production method is $220 per hour.b. What is
7. Carpetland salespersons average $8000 per week in sales. Steve Contois, the firm’s vice president, proposes a compensation plan with new selling incentives. Steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales
6. The label on a 3-quart container of orange juice claims that the orange juice contains an average of 1 gram of fat or less. Answer the following questions for a hypothesis test that could be used to test the claim on the label.a. Develop the appropriate null and alternative hypotheses.
5. Nielsen reported that young men in the United States watch 56.2 minutes of prime-time TV daily (The Wall Street Journal Europe, November 18, 2003). A researcher believes that young men in Germany spend more time watching prime-time TV. A sample of German young men will be selected by the
4. Because of high production-changeover time and costs, a director of manufacturing must convince management that a proposed manufacturing method reduces costs before the new method can be implemented. The current production method operates with a mean cost of$220 per hour. A research study will
3. A production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of cartons is periodically selected and weighed to determine whether underfilling or overfilling is occurring. If the sample data lead to a conclusion of underfilling or
2. The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean sales volume is 14 automobiles per month. The manager wants to conduct a research study to see whether the new bonus plan increases sales volume. To collect data on the
1. The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel’s accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of weekend guest bills
5. What other information would you like to gather to evaluate the transmission failure problem more fully?
4. How many repair records should be sampled if the research firm wants the population mean number of miles driven until transmission failure to be estimated with a margin of error of 5000 miles? Use 95% confidence.
3. Discuss the implication of your statistical findings in terms of the belief that some owners of the automobiles experienced early transmission failures.
2. Develop a 95% confidence interval for the mean number of miles driven until transmission failure for the population of automobiles with transmission failure. Provide a managerial interpretation of the interval estimate.
1. Use appropriate descriptive statistics to summarize the transmission failure data.
60. Although airline schedules and cost are important factors for business travelers when choosing an airline carrier, a USA Today survey found that business travelers list an airline’s frequent flyer program as the most important factor. From a sample of n 1993 business travelers who responded
59. In a survey, 200 people were asked to identify their major source of news information; 110 stated that their major source was television news.a. Construct a 95% confidence interval for the proportion of people in the population who consider television their major source of news information.b.
58. A well-known bank credit card firm wishes to estimate the proportion of credit card holders who carry a nonzero balance at the end of the month and incur an interest charge.Assume that the desired margin of error is .03 at 98% confidence.a. How large a sample should be selected if it is
57. The 2003 Statistical Abstract of the United States reported the percentage of people 18 years of age and older who smoke. Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .30.a. How large a sample should be
56. Cincinnati/Northern Kentucky International Airport had the second highest on-time arrival rate for 2005 among the nation’s busiest airports (The Cincinnati Enquirer, February 3, 2006). Assume the findings were based on 455 on-time arrivals out of a sample of 550 flights.a. Develop a point
55. Which would be hardest for you to give up: Your computer or your television? In a recent survey of 1677 U.S. Internet users, 74% of the young tech elite (average age of 22) say their computer would be very hard to give up (PC Magazine, February 3, 2004). Only 48%say their television would be
54. An Employee Benefits Research Institute survey of 1250 workers over the age of 25 collected opinions on the health care system in America and on retirement planning (AARP Bulletin, January 2007).a. The American health care system was rated as poor by 388 of the respondents. Construct a 95%
53. The National Center for Education Statistics reported that 47% of college students work to pay for tuition and living expenses. Assume that a sample of 450 college students was used in the study.a. Provide a 95% confidence interval for the population proportion of college students who work to
52. Annual salary plus bonus data for chief executive officers are presented in the BusinessWeek Annual Pay Survey. A preliminary sample showed that the standard deviation is $675 with data provided in thousands of dollars. How many chief executive officers should be in a sample if we want to
51. In developing patient appointment schedules, a medical center wants to estimate the mean time that a staff member spends with each patient. How large a sample should be taken if the desired margin of error is two minutes at a 95% level of confidence? How large a sample should be taken for a 99%
50. Mileage tests are conducted for a particular model of automobile. If a 98% confidence interval with a margin of error of 1 mile per gallon is desired, how many automobiles should be used in the test? Assume that preliminary mileage tests indicate the standard deviation is 2.6 miles per gallon.
49. A survey by Accountemps asked a sample of 200 executives to provide data on the number of minutes per day office workers waste trying to locate mislabeled, misfiled, or misplaced items. Data consistent with this survey are contained in the data set ActTemps.a. Use ActTemps to develop a point
48. US Airways conducted a number of studies that indicated a substantial savings could be obtained by encouraging Dividend Miles frequent flyer customers to redeem miles and schedule award flights online (US Airways Attaché, February 2003). One study collected data on the amount of time required
47. Many stock market observers say that when the P/E ratio for stocks gets over 20 the market is overvalued. The P/E ratio is the stock price divided by the most recent 12 months of earnings.Suppose you are interested in seeing whether the current market is overvalued and would also like to know
46. The motion picture Harry Potter and the Sorcerer’s Stone shattered the box office debut record previously held by The Lost World: Jurassic Park (The Wall Street Journal, November 19, 2001). A sample of 100 movie theaters showed that the mean three-day weekend gross was $25,467 per theater.
45. A survey conducted by the American Automobile Association showed that a family of four spends an average of $215.60 per day while on vacation. Suppose a sample of 64 families of four vacationing at Niagara Falls resulted in a sample mean of $252.45 per day and a sample standard deviation of
44. A sample survey of 54 discount brokers showed that the mean price charged for a trade of 100 shares at $50 per share was $33.77 (AAII Journal, February 2006). The survey is conducted annually. With the historical data available, assume a known population standard deviation of $15.a. Using the
43. APhoenix Wealth Management/Harris Interactive survey of 1500 individuals with net worth of $1 million or more provided a variety of statistics on wealthy people (BusinessWeek, September 22, 2003). The previous three-year period had been bad for the stock market, which motivated some of the
42. A USA Today/CNN/Gallup poll for the presidential campaign sampled 491 potential voters in June (USA Today, June 9, 2000). A primary purpose of the poll was to obtain an estimate of the proportion of potential voters who favor each candidate. Assume a planning value of p* .50 and a 95%
41. America’s young people are heavy Internet users; 87% of Americans ages 12 to 17 are Internet users (The Cincinnati Enquirer, February 7, 2006). MySpace was voted the most popular Web site by 9% in a sample survey of Internet users in this age group. Suppose 1400 youths participated in the
40. The professional baseball home run record of 61 home runs in a season was held for 37 years by Roger Maris of the New York Yankees. However, between 1998 and 2001, three players—Mark McGwire, Sammy Sosa, and Barry Bonds—broke the standard set by Maris, with Bonds holding the current record
39. The percentage of people not covered by health care insurance in 2003 was 15.6% (Statistical Abstract of the United States, 2006). A congressional committee has been charged with conducting a sample survey to obtain more current information.a. What sample size would you recommend if the
38. According to Thomson Financial, through January 25, 2006, the majority of companies reporting profits had beaten estimates (BusinessWeek, February 6, 2006). A sample of 162 companies showed 104 beat estimates, 29 matched estimates, and 29 fell short.a. What is the point estimate of the
37. Towers Perrin, a New York human resources consulting firm, conducted a survey of 1100 employees at medium-sized and large companies to determine how dissatisfied employees were with their jobs (The Wall Street Journal, January 29, 2003). Representative data are shown in the file
36. According to statistics reported on CNBC, a surprising number of motor vehicles are not covered by insurance (CNBC, February 23, 2006). Sample results, consistent with the CNBC report, showed 46 of 200 vehicles were not covered by insurance.a. What is the point estimate of the proportion of
35. Asurvey of 611 office workers investigated telephone answering practices, including how often each office worker was able to answer incoming telephone calls and how often incoming telephone calls went directly to voice mail (USA Today, April 21, 2002). A total of 281 office workers indicated
34. At 95% confidence, how large a sample should be taken to obtain a margin of error of .03 for the estimation of a population proportion? Assume that past data are not available for developing a planning value for p*.
33. In a survey, the planning value for the population proportion is p* .35. How large a sample should be taken to provide a 95% confidence interval with a margin of error of .05?
32. A simple random sample of 800 elements generates a sample proportion .70.a. Provide a 90% confidence interval for the population proportion.b. Provide a 95% confidence interval for the population proportion.
31. A simple random sample of 400 individuals provides 100 Yes responses.a. What is the point estimate of the proportion of the population that would provide Yes responses?b. What is your estimate of the standard error of the proportion, ?c. Compute the 95% confidence interval for the population
30. During the first quarter of 2003, the price/earnings (P/E) ratio for stocks listed on the New York Stock Exchange generally ranged from 5 to 60 (The Wall Street Journal, March 7, 2003). Assume that we want to estimate the population mean P/E ratio for all stocks listed on the exchange. How many
29. The travel-to-work time for residents of the 15 largest cities in the United States is reported in the 2003 Information Please Almanac. Suppose that a preliminary simple random sample of residents of San Francisco is used to develop a planning value of 6.25 minutes for the population standard
28. An online survey by ShareBuilder, a retirement plan provider, and Harris Interactive reported that 60% of female business owners are not confident they are saving enough for retirement (SmallBiz, Winter 2006). Suppose we would like to do a follow-up study to determine how much female business
27. Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $30,000 and $45,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. What is the planning value for the population
26. The average cost of a gallon of unleaded gasoline in Greater Cincinnati was reported to be$2.41 (The Cincinnati Enquirer, February 3, 2006). During periods of rapidly changing prices, the newspaper samples service stations and prepares reports on gasoline prices frequently. Assume the standard
25. Refer to the Scheer Industries example in Section 8.2. Use 6.84 days as a planning value for the population standard deviation.a. Assuming 95% confidence, what sample size would be required to obtain a margin of error of 1.5 days?b. If the precision statement was made with 90% confidence, what
24. The range for a set of data is estimated to be 36.a. What is the planning value for the population standard deviation?b. At 95% confidence, how large a sample would provide a margin of error of 3?c. At 95% confidence, how large a sample would provide a margin of error of 2?
23. How large a sample should be selected to provide a 95% confidence interval with a margin of error of 10? Assume that the population standard deviation is 40.
22. The first few weeks of 2004 were good for the stock market. A sample of 25 large openend funds showed the following year-to-date returns through January 16, 2004 (Barron’s, January 19, 2004).7.0 3.2 1.4 5.4 8.5 2.5 2.5 1.9 5.4 1.6 1.0 2.1 8.5 4.3 6.2 1.5 1.2 2.7 3.8 2.0 1.2 2.6 4.0 2.6 0.6a.
21. Consumption of alcoholic beverages by young women of drinking age has been increasing in the United Kingdom, the United States, and Europe (The Wall Street Journal, February 15, 2006). Data (annual consumption in liters) consistent with the findings reported in The Wall Street Journal article
20. Is your favorite TV program often interrupted by advertising? CNBC presented statistics on the average number of programming minutes in a half-hour sitcom (CNBC, February 23, 2006). The following data (in minutes) are representative of their findings.21.06 22.24 20.62 21.66 21.23 23.86 23.82
19. A National Retail Foundation survey found households intended to spend an average of$649 during the December holiday season (The Wall Street Journal, December 2, 2002). Assumethatthesurveyincluded600householdsandthatthesamplestandarddeviationwas$175.a. With 95% confidence, what is the margin of
18. Thirty fast-food restaurants including Wendy’s, McDonald’s, and Burger King were visited during the summer of 2000 (The Cincinnati Enquirer, July 9, 2000). During each visit, the customer went to the drive-through and ordered a basic meal such as a “combo” meal or a sandwich, fries, and
17. The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the
16. The mean number of hours of flying time for pilots at Continental Airlines is 49 hours per month (The Wall Street Journal, February 25, 2003). Assume that this mean was based on actual flying times for a sample of 100 Continental pilots and that the sample standard deviation was 8.5 hours.a. At
15. Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 65 weekly reports showed a sample mean of 19.5 customer contacts per week. The sample standard deviation was 5.2. Provide 90% and 95%confidence intervals for the
14. A simple random sample with n 54 provided a sample mean of 22.5 and a sample standard deviation of 4.4.a. Develop a 90% confidence interval for the population mean.b. Develop a 95% confidence interval for the population mean.c. Develop a 99% confidence interval for the population mean.d. What
13. The following sample data are from a normal population: 10, 8, 12, 15, 13, 11, 6, 5.a. What is the point estimate of the population mean?b. What is the point estimate of the population standard deviation?c. With 95% confidence, what is the margin of error for the estimation of the population
12. Find the t value(s) for each of the following cases.a. Upper tail area of .025 with 12 degrees of freedomb. Lower tail area of .05 with 50 degrees of freedomc. Upper tail area of .01 with 30 degrees of freedomd. Where 90% of the area falls between these two t values with 25 degrees of freedome.
11. For a t distribution with 16 degrees of freedom, find the area, or probability, in each region.a. To the right of 2.120b. To the left of 1.337c. To the left of 1.746d. To the right of 2.583e. Between 2.120 and 2.120f. Between 1.746 and 1.746
10. Playbill magazine reported that the mean annual household income of its readers is$119,155 (Playbill, January 2006). Assume this estimate of the mean annual household income is based on a sample of 80 households, and based on past studies, the population standard deviation is known to be σ
9. The undergraduate grade point average (GPA) for students admitted to the top graduate business schools was 3.37 (Best Graduate Schools, U.S. News and World Report, 2001).Assume this estimate was based on a sample of 120 students admitted to the top schools.Using past years’ data, the
8. The National Quality Research Center at the University of Michigan provides a quarterly measure of consumer opinions about products and services (The Wall Street Journal, February 18, 2003). A survey of 10 restaurants in the Fast Food/Pizza group showed a sample mean customer satisfaction index
7. A survey of small businesses with Web sites found that the average amount spent on a site was $11,500 per year (Fortune, March 5, 2001). Given a sample of 60 businesses and a population standard deviation of σ $4000, what is the margin of error? Use 95% confidence. What would you recommend if
6. Nielsen Media Research conducted a study of household television viewing times during the 8 p.m. to 11 p.m. time period. The data contained in the CD file named Nielsen are consistent with the findings reported (The World Almanac, 2003). Based upon past studies the population standard deviation
5. In an effort to estimate the mean amount spent per customer for dinner at a major Atlanta restaurant, data were collected for a sample of 49 customers. Assume a population standard deviation of $5.a. At 95% confidence, what is the margin of error?b. If the sample mean is $24.80, what is the 95%
4. A 95% confidence interval for a population mean was reported to be 152 to 160. If σ 15, what sample size was used in this study?
3. A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is σ 15.a. Compute the 95% confidence interval for the population mean.b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the
2. A simple random sample of 50 items from a population with σ 6 resulted in a sample mean of 32.a. Provide a 90% confidence interval for the population mean.b. Provide a 95% confidence interval for the population mean.c. Provide a 99% confidence interval for the population mean.
1. A simple random sample of 40 items resulted in a sample mean of 25. The population standard deviation is σ 5.a. What is the standard error of the mean, ?b. At 95% confidence, what is the margin of error?
54. Lori Jeffrey is a successful sales representative for a major publisher of college textbooks.Historically, Lori obtains a book adoption on 25% of her sales calls. Viewing her sales calls for one month as a sample of all possible sales calls, assume that a statistical analysis of the data yields
53. The proportion of individuals insured by the All-Driver Automobile Insurance Company who received at least one traffic ticket during a five-year period is .15.a. Show the sampling distribution of if a random sample of 150 insured individuals is used to estimate the proportion having received at
52. Advertisers contract with Internet service providers and search engines to place ads on Web sites. They pay a fee based on the number of potential customers who click on their ad. Unfortunately, click fraud—the practice of someone clicking on an ad solely for the purpose of driving up
51. A market research firm conducts telephone surveys with a 40% historical response rate.What is the probability that in a new sample of 400 telephone numbers, at least 150 individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion
50. About 28% of private companies are owned by women (The Cincinnati Enquirer, January 26, 2006). Answer the following questions based on a sample of 240 private companies.a. Show the sampling distribution of , the sample proportion of companies that are owned by women.b. What is the probability
49. A production process is checked periodically by a quality control inspector. The inspector selects simple random samples of 30 finished products and computes the sample mean product weights . If test results over a long period of time show that 5% of the values are over 2.1 pounds and 5% are
48. A researcher reports survey results by stating that the standard error of the mean is 20. The population standard deviation is 500.a. How large was the sample used in this survey?b. What is the probability that the point estimate was within 25 of the population mean?
47. Three firms carry inventories that differ in size. Firm A’s inventory contains 2000 items, firm B’s inventory contains 5000 items, and firm C’s inventory contains 10,000 items. The population standard deviation for the cost of the items in each firm’s inventory is σ 144.A statistical
46. The average credit card balance for college seniors is $2864 (CNBC, October 19, 2006). Use this figure as the population mean and assume the population standard deviation is σ $775.Suppose that a random sample of 50 college seniors will be selected from the population.a. What is the value of
45. The mean television viewing time for Americans is 15 hours per week (Money, November 2003). Suppose a sample of 60 Americans is taken to further investigate viewing habits.Assume the population standard deviation for weekly viewing time is σ 4 hours.a. What is the probability the sample mean
44. BusinessWeek surveyed MBAalumni 10 years after graduation (BusinessWeek, September 22, 2003). One finding was that alumni spend an average of $115.50 per week eating out socially. You have been asked to conduct a follow-up study by taking a sample of 40 of these MBA alumni. Assume the
43. Americans have become increasingly concerned about the rising cost of Medicare. In 1990, the average annual Medicare spending per enrollee was $3267; in 2003, the average annual Medicare spending per enrollee was $6883 (Money, Fall 2003). Suppose you hired a consulting firm to take a sample of
42. BusinessWeek’s Corporate Scoreboard provides quarterly data on sales, profits, net income, return on equity, price/earnings ratio, and earnings per share for 899 companies (BusinessWeek, August 14, 2000). The companies can be numbered 1 to 899 in the order they appear on the Corporate
41. The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p .17 and a simple random sample of 800 households will be selected from the population.a. Show the sampling distribution of , the sample proportion of
40. The Grocery Manufacturers of America reported that 76% of consumers read the ingredients listed on a product’s label. Assume the population proportion is p .76 and a sample of 400 consumers is selected from the population.a. Show the sampling distribution of the sample proportion where is
39. The Democrat and Chronicle reported that 25% of the flights arriving at the San Diego airport during the first five months of 2001 were late (Democrat and Chronicle, July 23, 2001). Assume the population proportion is p .25.a. Show the sampling distribution of , the proportion of late flights
38. Roper ASW conducted a survey to learn about American adults’ attitudes toward money and happiness (Money, October 2003). Fifty-six percent of the respondents said they balance their checkbook at least once a month.a. Suppose a sample of 400 American adults were taken. Show the sampling
37. Time/CNN voter polls monitored public opinion for the presidential candidates during the 2000 presidential election campaign. One Time/CNN poll conducted by Yankelovich Partners, Inc., used a sample of 589 likely voters (Time, June 26, 2000). Assume the population proportion for a presidential
36. The Cincinnati Enquirer reported that, in the United States, 66% of adults and 87% of youths ages 12 to 17 use the Internet (The Cincinnati Enquirer, February 7, 2006). Use the reported numbers as the population proportions and assume that samples of 300 adults and 300 youths will be used to
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