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essentials of statistics
Questions and Answers of
Essentials Of Statistics
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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,
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
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%
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,
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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,
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
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
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).
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
35. The president of Doerman Distributors, Inc., believes that 30% of the firm’s orders come from first-time customers. A simple random sample of 100 orders will be used to estimate the proportion
34. The population proportion is .30. What is the probability that a sample proportion will be within .04 of the population proportion for each of the following sample sizes?a. n 100b. n 200c. n
33. Assume that the population proportion is .55. Compute the standard error of the proportion, , for sample sizes of 100, 200, 500, and 1000. What can you say about the size of the standard error of
32. A population proportion is .40. A simple random sample of size 200 will be taken and the sample proportion will be used to estimate the population proportion.a. What is the probability that the
31. A simple random sample of size 100 is selected from a population with p .40.a. What is the expected value of ?b. What is the standard error of ?c. Show the sampling distribution of .d. What
30. To estimate the mean age for a population of 4000 employees, a simple random sample of 40 employees is selected.a. Would you use the finite population correction factor in calculating the
29. The average price of a gallon of unleaded regular gasoline was reported to be $2.34 in northern Kentucky (The Cincinnati Enquirer, January 21, 2006). Use this price as the population mean, and
28. The average score for male golfers is 95 and the average score for female golfers is 106(Golf Digest, April 2006). Use these values as the population means for men and women and assume that the
27. BusinessWeek conducted a survey of graduates from 30 top MBA programs (BusinessWeek, September 22, 2003). On the basis of the survey, assume that the mean annual salary for male and female
26. The mean annual cost of automobile insurance is $939 (CNBC, February 23, 2006).Assume that the standard deviation is σ $245.a. What is the probability that a simple random sample of automobile
25. The College Board American College Testing Program reported a population mean SAT score of μ 1020 (The World Almanac 2003). Assume that the population standard deviation is σ 100.a. What is
24. The mean tuition cost at state universities throughout the United States is $4260 per year(St. Petersburg Times, December 11, 2002). Use this value as the population mean and assume that the
23. In the EAI sampling problem (see Figure 7.5), we showed that for n 30, there was .5034 probability of obtaining a sample mean within $500 of the population mean.a. What is the probability that
22. Refer to the EAI sampling problem. Suppose a simple random sample of 60 managers is used.a. Sketch the sampling distribution of when simple random samples of size 60 are used.b. What happens to
21. Suppose a simple random sample of size 50 is selected from a population with σ 10.Find the value of the standard error of the mean in each of the following cases (use the finite population
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