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business
business statistics a first course

Questions and Answers of Business Statistics A First Course

10.77 Using the sample results in Exercise 10.76, construct and interpret the 90% confidence interval for the population proportion. Is the hypothesized proportion(0.41) within the interval? Given
10.76 According to the National Collegiate Athletic Association (NCAA), 41% of male basketball players graduate within 6 years of enrolling in their college or university, compared to 56% for the
10.75 Based on the sample results in Exercise 10.74, construct and interpret the 90% confidence interval for the population proportion. Is the hypothesized proportion(0.80) within the interval? Given
10.74 It has been reported that 80% of taxpayers who are audited by the Internal Revenue Service end up paying more money in taxes. Assume that auditors are randomly assigned to cases, and that one
10.73 Brad Davenport, a consumer reporter for a national cable TV channel, is working on a story evaluating generic food products and comparing them to their brand-name counterparts. According to
10.72 Using the sample results in Exercise 10.71, construct and interpret the 90% confidence interval for the population proportion. Is the hypothesized population proportion (0.07) within the
10.71 According to the U.S. Bureau of Labor Statistics, 7.0% of female hourly workers who are 16 to 24 years old are being paid minimum wage or less. (Note that some workers in some industries are
10.70 Based on the sample results in Exercise 10.69, construct and interpret the 95% confidence interval for the population proportion. Is the hypothesized proportion(0.55) within the interval? Given
10.68 Heritage Union has said that 66% of U.S. adults have purchased life insurance. Suppose that for a random sample of 50 adults from a given U.S. city, a researcher finds that only 56% of them
10.67 In the past, 44% of those taking a public accounting qualifying exam have passed the exam on their first try. Lately, the availability of exam preparation books and tutoring sessions may have
10.66 It has been claimed that 65% of homeowners would prefer to heat with electricity instead of gas. A study finds that 60% of 200 homeowners prefer electric heating to gas. In a two-tail test at
10.65 According to the human resources director of a plant, no more than 5% of employees hired in the past year have violated their preemployment agreement not to use any of five illegal drugs. The
10.64 The director of admissions at a large university says that 15% of high school juniors to whom she sends university literature eventually apply for admission. In a sample of 300 persons to whom
10.63 A simple random sample of 300 items is selected from a large shipment, and testing reveals that 4% of the sampled items are defective. The supplier claims that no more than 2% of the items in
10.62 For a simple random sample, n 5 700 and p 5 0.63. At the 0.025 level, test H0: # 0.60 versus H1: . 0.60.
10.61 For a simple random sample, n 5 1000 and p 5 0.47. At the 0.05 level, test H0: $ 0.50 versus H1: , 0.50.
For a simple random sample, n 5 200 and p 5 0.34.At the 0.01 level, test H0: 5 0.40 versus H1: 0.40.
When carrying out a hypothesis test for a population proportion, under what conditions is it appropriate to use the normal distribution as an approximation to the (theoretically correct) binomial
10.58 Using the sample data in Exercise 10.57, construct and interpret the 95% confidence interval for the popula tion mean. Is the hypothesized population mean($817) within the interval? Given the
10.57 According to the Insurance Information Institute, the mean annual expenditure for automobile insurance for U.S. motorists is $817. Suppose that a government official in North Carolina has
10.56 The International Council of Shopping Centers reports that the average teenager spends $57 during a shopping trip to the mall. The promotions director of a local mall has used a variety of
10.55 Using the sample results in Exercise 10.54, construct and interpret the 90% confidence interval for the population mean. Is the hypothesized population mean(38 minutes) within the interval?
10.54 The U.S. Census Bureau says the 52-question“long form” received by 1 in 6 households during the 2000 census takes a mean of 38 minutes to complete.Suppose a simple random sample of 35
10.53 Using the sample results in Exercise 10.52, construct and interpret the 95% confidence interval for the population mean. Is the hypothesized population mean(93 seconds) within the interval?
10.52 In response to an inquiry from its national office, the manager of a local bank has stated that her bank’s average service time for a drive-through customer is 93 seconds. A student intern
10.51 It has been reported that the average life for halogen lightbulbs is 4000 hours. Learning of this figure, a plant manager would like to find out whether the vibration and temperature conditions
10.50 Using the sample results in Exercise 10.49, construct and interpret the 95% confidence interval for the population mean. Is the hypothesized population mean($640,000) within the interval? Given
10.49 According to the Federal Reserve Board, the mean net worth of U.S. households headed by persons 75 years or older is $640,000. Suppose a simple random sample of 50 households in this age group
10.48 During 2008, college work-study students earned a mean of $1478. Assume that a sample consisting of 45 of the work-study students at a large university was found to have earned a mean of $1503
10.47 A scrap metal dealer claims that the mean of his cash sales is “no more than $80,” but an Inter nal Revenue Service agent believes the dealer is untruthful.Observing a sample of 20 cash
10.46 The new director of a local YMCA has been told by his predecessors that the average member has belonged for 8.7 years. Examining a random sample of 15 membership files, he finds the mean length
10.45 Taxco, a firm specializing in the preparation of income tax returns, claims the mean refund for customers who received refunds last year was $150. For a random sample of 12 customers who
10.44 The International Coffee Association has reported the mean daily coffee consumption for U.S. residents as 1.65 cups. Assume that a sample of 38 people from a North Carolina city consumed a mean
10.43 The average length of a flight by regional airlines in the United States has been reported as 464 miles. If a simple random sample of 30 flights by regional airlines were to have }x 5 479.6
10.42 The average age of passenger cars in use in the United States is 9.0 years. For a simple random sample of 34 vehicles observed in the employee parking area of a large manufacturing plant, the
10.41 For a simple random sample of 15 items from a population that is approximately normally distributed,}x 5 82.0 and s 5 20.5. At the 0.05 level of significance, test H0: $ 90.0 versus H1: ,
10.40 For a simple random sample of 40 items, }x 5 25.9 and s 5 4.2. At the 0.01 level of significance, test H0: 5 24.0 versus H1: 24.0.
10.39 Under what circumstances should the t-statistic be used in carrying out a hypothesis test for the population mean?
10.38 Use an appropriate confidence interval in reaching a conclusion regarding the problem situation and null hypothesis for Exercise 10.31.
10.37 Given the information in Exercise 10.29, construct a 99% confidence interval for the population mean, then reach a conclusion regarding whether could actually be equal to the value that has
10.36 Given the information in Exercise 10.27, construct a 95% confidence interval for the population mean, then reach a conclusion regarding whether could actually be equal to the value that has
10.35 Based on sample data, a confidence interval has been constructed such that we have 90% confidence that the population mean is between 120 and 180. Given this information, provide the conclusion
10.34 A machine that fills shipping containers with driveway filler mix is set to deliver a mean fill weight of 70.0 pounds. The standard deviation of fill weights delivered by the machine is known
10.33 According to bankrate.com, the average cost to remodel a home office is $10,526. Assuming a population standard deviation of $2000 and the sample of home office conversion prices charged for 40
10.32 A manufacturer of electronic kits has found that the mean time required for novices to assemble its new circuit tester is 3 hours, with a standard deviation of 0.20 hours. A consultant has
10.31 Following maintenance and calibration, an extrusion machine produces aluminum tubing with a mean outside diameter of 2.500 inches, with a standard deviation of 0.027 inches. As the machine
10.30 In the past, patrons of a cinema complex have spent an average of $5.00 for popcorn and other snacks, with a standard deviation of $1.80. The amounts of these expenditures have been normally
10.29 A quality-assurance inspector periodically examines the output of a machine to determine whether it is properly adjusted. When set properly, the machine produces nails having a mean length of
10.28 For a sample of 12 items from a normally distributed population for which the standard deviation is 5 17.0, the sample mean is 230.8. At the 0.05 level of significance, test H0: # 220 versus
10.27 For a sample of 35 items from a population for which the standard deviation is 5 20.5, the sample mean is 458.0. At the 0.05 level of significance, test H0: 5 450 versus H1: 450.
10.26 For each of the following tests and z values, determine the p-value for the test:a. Left-tail test and z 5 21.62b. Right-tail test and z 5 1.43c. Two-tail test and z 5 1.27
10.25 For each of the following tests and z values, determine the p-value for the test:a. Right-tail test and z 5 1.54b. Left-tail test and z 5 21.03c. Two-tail test and z 5 21.83
10.24 A hypothesis test is carried out using the 5 0.01 level of significance, and H0 cannot be rejected. What is the most accurate statement we can make about the p-value for this test?
10.23 The p-value for a hypothesis test has been reported as 0.04. If the test result is interpreted using the 5 0.01 level of significance as a criterion, will H0 be rejected? Explain.
10.22 The p-value for a hypothesis test has been reported as 0.03. If the test result is interpreted using the 5 0.05 level of significance as a criterion, will H0 be rejected? Explain.
10.21 What is a p-value, and how is it relevant to hypothesis testing?
10.20 If the population standard deviation is known, but the sample size is less than 30, what assumption is necessary to use the z-statistic in carrying out a hypothesis test for the population mean?
10.19 What is the central limit theorem, and how is it applicable to hypothesis testing?
10.18 It has been claimed that no more than 5% of the units coming off an assembly line are defective.Formulate a null hypothesis and an alternative hypothesis for this situation. Will the test be
10.17 A manufacturer informs a customer’s design engineers that the mean tensile strength of its rivets is at least 3000 pounds. A test is set up to measure the tensile strength of a sample of
10.16 In hypothesis testing, what is meant by the decision rule? What role does it play in the hypothesistesting procedure?
10.15 A research firm claims that 62% of women in the 40–49 age group save in a 401(k) or individual retirement account. If we wished to test whether this percentage could be the same for women in
10.14 A researcher wants to carry out a hypothesis test involving the mean for a sample of size n 5 18. She does not know the true value of the population standard deviation, but is reasonably sure
10.13 Regarding the testing of pharmaceutical companies’claims that their drugs are safe, a U.S. Food and Drug Administration official has said that it’s “better to turn down 1000 good drugs
10.12 In the judicial system, the defense attorney argues for the null hypothesis that the defendant is innocent.In general, what would be the result if judges instructed juries toa. never make a
10.11 In administering a “field sobriety” test to suspected drunks, officers may ask a person to walk in a straight line or close his eyes and touch his nose. Define the Type I and Type II errors
10.10 For each of the following statements, formulate appropriate null and alternative hypotheses. Indicate whether the appropriate test will be one-tail or twotail, then sketch a diagram that shows
10.9 In response to the assertion made in Exercise 10.8, suppose an insurance company executive were to claim the percentage of fraudulent auto theft reports to be “no more than 10%.” What null
10.8 A state representative is reported as saying that about 10% of reported auto thefts involve owners whose cars have not really been stolen, but who are trying to defraud their insurance company.
10.7 Following a major earthquake, the city engineer must determine whether the stadium is structurally sound for an upcoming athletic event. If the null hypothesis is“the stadium is structurally
10.6 Many law enforcement agencies use voice-stress analysis to help determine whether persons under interrogation are lying. If the sound frequency of a person’s voice changes when asked a
10.5 On CNN and other news networks, guests often express their opinions in rather strong, persuasive, and sometimes frightening terms. For example, a scientist who strongly believes that global
10.4 The president of a company that manufactures central home air conditioning units has told an investigative reporter that at least 85% of its homeowner customers claim to be “completely
10.3 For each of the following pairs of null and alternative hypotheses, determine whether the pair would be appropriate for a hypothesis test. If a pair is deemed inappropriate, explain why.a. H0:
10.2 For each of the following pairs of null and alternative hypotheses, determine whether the pair would be appropriate for a hypothesis test. If a pair is deemed inappropriate, explain why.a. H0:
10.1 What is the difference between a null hypothesis and an alternative hypothesis? Is the null hypothesis always the same as the verbal claim or assertion that led to the test? Why or why not?
11.4 With the slider set so that df 5 9, enter 0.10 into the twotail probability text box at the right. What value of t now appears in the left text box? To what right-tail area does this
11.3 Position the slider so that df 5 2, then gradually move it upward until df 5 100. Describe how the value in the t text box and the shape of the t distribution change along the way.
11.2 Gradually move the slider upward until df 5 89.What effect does this have on the t value shown in the text box?
11.1 With the slider set so that df 5 9 and the left text box containing t 5 3.25, what is the area beneath the curve between t 5 23.25 and t 5 13.25?
10.4 Position the slider so that df 5 2, then gradually move it upward until df 5 100. Describe how the shape of the t distribution changes along the way.
10.3 Gradually move the slider upward so that df increases from 2 to 10. Describe how the shape of the t distribution changes along the way.
10.2 Move the slider downward so that df 5 2. How has this decrease changed the shape of the t distribution?
10.1 Move the slider so that df 5 5. Describe the shape of the t distribution compared to that of the standard normal distribution.
9.4 Position the slider at its extreme left position, then gradually move it to the far right. Describe how this movement changes the confidence level and the width of the confidence interval.
9.3 Move the slider so that the confidence interval is now 80%. Describe how the decrease in the confidence level has changed the width of the confidence interval.
9.2 Move the slider so that the confidence interval is now 99%. Describe how the increase in the confidence level has changed the width of the confidence interval.
9.1 With the slider positioned so as to specify a 95%confidence interval for , what are the upper and lower confidence limits?
9.1 Given the breakdown of responses for variable 28(marital status of respondent), determine the point estimate, then construct the 95% confidence interval for 28 5 the population proportion in the
9.1 Given the breakdown of responses for variable 26(sex of respondent), determine the point estimate, then construct the 95% confidence interval for 26 5 the population proportion of males. What is
9.1 Item C in the description of the data collection instrument lists variables 7, 8, and 9, which represent the respondent’s general attitude toward each of the three shopping areas. Each of these
9.111 To avoid losing part of their federal highway fund allocation, state safety administrators must ensure that interstate speed limits are adequately enforced within their state. In an upcoming
9.110 According to the Internal Revenue Service, the average deduction for charitable contributions in the most recent tax year reported was $4388. Curious to see how his legislative district
9.109 It has been estimated that the average dinner check at Morton’s, the world’s largest chain of upscale steakhouses, is $97 per person. Such a finding could have been based on data like the
9.108 A researcher has estimated that U.S. college students spend an average of 17.2 hours per week on the Internet. Assuming a simple random sample of 500 college students and a sample standard
9.107 A truck loaded with 8000 electronic circuit boards has just pulled into a firm’s receiving dock. The supplier claims that no more than 3% of the boards fall outside the most rigid level of
9.106 A researcher, believing to be no more than 0.40, calculates the necessary sample size for the confidence level and maximum likely error he has specified. Upon completing the study, he finds
9.105 A survey of business travelers found that 40% of those surveyed utilize hotel exercise facilities during their stay. Under the assumption that a simple random sample of 1000 business travelers
9.104 To gain information about competitors’ products, companies sometimes employ “reverse engineering,”which consists of buying the competitor’s product, then taking it apart and examining
9.103 The Colgate-Palmolive Company has 36,600 employees. If the company wishes to estimate, within 2 percentage points and with 99% confidence, the percentage of employees who are interested in

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