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business statistics a first course
Introduction To Business Statistics 7th Edition Ronald M. Weiers - Solutions
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 miles and s 5 42.8 miles, would this tend to cast doubt on the reported average of 464 miles? Use a
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 average age is 10.4 years, with a standard deviation of 3.1 years. At the 0.01 level of significance,
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: , 90.0.
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 been hypothesized. How does this conclusion compare to that reached in Exercise 10.29? Why?
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 been hypothesized. How does this conclusion compare to that reached in Exercise 10.27? Why?
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 that would be reached for each of the following hypothesis tests at the 5 0.10 level:a. H0: 5
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 to be 1.0 pounds. For a recent sample of 35 containers, the fill weights are listed in data file
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 recent jobs performed by builders in a region of the United States, examine whether the mean price
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 developed a new instructional booklet intended to reduce the time an inexperienced kit builder will need
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 functions over an extended number of work shifts, the standard deviation remains unchanged, but the
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 distributed. Following an intensive publicity campaign by a local medical society, the mean
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 2.000 inches, with a standard deviation of 0.070 inches. For a sample of 35 nails, the mean length is
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 H1: . 220.Determine and interpret the p-value for the test.
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. Determine and interpret the p-value for the test.
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 one-tail or two-tail? Why? If the test is one-tail, will it be left-tail or right-tail? Why?
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 rivets, with the null and alternative hypotheses, H0: $ 3000 and H1: , 3000. For each of the
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 this age group living in New York City and selected a random sample of 300 such individuals from New
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 that the underlying population is approximately normally distributed. Should she use a z-test or a
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 than to approve one that’s unsafe.” If the null hypothesis is H0: “The drug is not harmful,”
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 Type I error?b. never make a Type II error?c. compromise between Type I and Type II errors?
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 in terms of this setting. Speculate on physiological variables (besides the drinking of alcoholic
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 the approximate location of the “rejection” region(s) for the test.a. “The average college
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 and alternative hypotheses would be appropriate in evaluating the executive’s statement?
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. What null and alternative hypotheses would be appropriate in evaluating the statement made by this
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 sound,” and the alternative hypothesis is “the stadium is not structurally sound,”which type of
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 question, the presumption is that the person is being untruthful. For this situation, state the null and
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 warming is taking place will warn us of the dire consequences (such as rising sea levels, coastal
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 satisfied” with the overall purchase experience. If the reporter were to subject the president’s
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: $ 0.30, H1: , 0.35b. H0: 5 0.72, H1: 0.72c. H0: # 0.25, H1: . 0.25d. H0: $ 0.48, H1:
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, H1: , 10b. H0: 5 30, H1: 30c. H0: . 90, H1: # 90d. H0: # 75, H1: # 85e. H0: }x
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 correspond?Verify the value of t for df 5 9 and this right-tail area by using the t table that precedes the
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 “single or other” category. What is the maximum likely error in the point estimate of 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 the maximum likely error in the point estimate of the population proportion?
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 variables has numerically equal distances between the possible responses, and for purposes of
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 test, federal researchers will be randomly selecting and clocking a very large sample of vehicles on a
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 compares, a state senator surveys a simple random sample of 200 taxpayers from the district, with the data
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 800 sample checks in file XR09109. Using the data in this file, construct and interpret the 95%
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 deviation of 1.4 hours per week, construct and interpret the 99%confidence interval for the population
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 industry performance specifications. In a simple random sample of 300 boards from this shipment, 12
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 the sample proportion to be 0.32. Is the maximum likely error greater than, equal to, or less than
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 were surveyed, construct and interpret the 90% and 95% confidence intervals for the proportion of
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 the parts in great detail. Engaging in this practice, a bicycle manufacturer intends to buy two or
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 participating in a new stock option benefits program, how large a simple random sample will be
9.102 In Exercise 9.101, suppose the tool manufacturer has carried out the study, using the sample size determined in that exercise, and 39.0% of the machinery rebuilding and repairing companies are interested in the new tool design. Construct and interpret the 95% confidence interval for the
9.101 There are 1254 machinery rebuilding and repairing companies in the United States. A tool manufacturer wishes to survey a simple random sample of these firms to find out what proportion of them are interested in a new tool design. If the tool manufacturer would like to be 95% confident that
9.100 A consultant conducts a pilot study to estimate a population standard deviation, then determines how large a simple random sample will be necessary to have a given level of confidence that the difference between }x and will be within the maxi mum error specified by her client. The necessary
9.99 An airline would like to determine, within 3 percentage points and with 95% confidence, the percentage of next month’s customers who judge the courtesy of its employees as being “very good to excellent.” What sample size would you recommend?
9.98 In a survey of 1320 executives who oversee corporate data systems, 24% said they had experienced losses caused by computer viruses during the past year.Assuming the executives were a simple random sample of all such executives, construct and interpret the 90% confidence inter val for the
9.97 A researcher would like to determine, within 3 percentage points and with 90% confidence, the percentage of Americans who have a certain characteristic. If she feels certain that the percentage is somewhere between 20%and 40%, how many persons should be included in the sample?
9.96 In a work-sampling study, an industrial engineer has observed the activities of a clerical worker on 121 randomly selected times during a workweek. On 32 of these occasions, the employee was talking on the telephone.For an 8-hour day, what are the upper and lower 95% confidence limits for the
9.95 The makers of Count Chocula breakfast cereal would like to determine, within 2 percentage points and with 99% confidence, the percentage of U.S. senior citizens who have Count Chocula for breakfast at least once a week. What sample size would you recommend?
9.94 For a process having a known standard deviation, a simple random sample of 35 items is selected. If the width of the 95% confidence interval is identified as y, express the width of the 99% confidence interval as a multiple of y.
9.93 A research firm has found that 39% of U.S. adults in the over-$75,000 income category work at least 51 hours per week. Assuming this was a simple random sample of 500 adults in this income group, construct and interpret the 95% and 99% confidence intervals for the proportion who work at least
9.92 The activities director of a large university has surveyed a simple random sample of 100 students for the purpose of determining approximately how many students to expect at next month’s awards ceremony to be held in the gymnasium. Forty of the students said they plan to attend. What are the
9.91 A research firm wants to be 90% confident that a population percentage has been estimated to within 3 percentage points. The research manager calculates the necessary sample size with 0.5 as his estimate of the population proportion. A new business school graduate who has just joined the firm
9.90 In Exercise 9.89, suppose Subway has carried out the study, using the sample size determined in that exercise, and 27.5% of the franchisees say they are pleased with their relationship with Subway. Construct and interpret the 95% confidence interval for the population percentage.
9.89 There were 904 new Subway Restaurants franchises opened during 2002. Suppose that Subway wished to survey a simple random sample of the new franchisees to find out what percentage of them were totally pleased with their relationship with the company.If Subway wanted to have 90% confidence in
9.88 For a new process with which the production personnel have little experience, neither the standard deviation nor the mean of the process is known.Twenty different simple random samples, each with n 5 50, are to be drawn from the process, and a 90%confidence interval for the mean is to be
9.87 For the following simple random sample of household incomes (thousands of dollars) from a large county, construct and interpret the 90% and 95% confidence intervals for the population mean. The data are also in file XR09087.58.3 50.0 58.1 33.5 51.1 38.1 42.3 60.4 55.8 46.2 40.4 52.5 51.3 47.5
9.86 In a survey of 500 U.S. adults, 45% of them said that lounging at the beach was their “dream vacation.”Assuming this to be a simple random sample of U.S.adults, construct and interpret the 95% and 99% confidence intervals for the proportion of U.S. adults who consider lounging at the beach
9.85 In Exercise 9.84, a small-scale preliminary survey has indicated that no more than 20% of the television households will tune in to the first episode of the miniseries. Given this information, how large must the sample be?
9.84 There are approximately 113 million television households in the United States. A ratings service would like to know, within 5 percentage points and with 95% confidence, the percentage of these households who tune in to the first epi sode of a network miniseries. How many television households
9.83 A torque wrench used in the final assembly of cylinder heads has a process standard deviation of 5.0 lb-ft.The engineers have specified that a process average of 135 lb-ft is desirable. For a simple random sample of 30 nuts that the machine has recently tightened, the sample mean is 137.0
9.82 The accompanying data represent one-way commuting times (minutes) for a simple random sample of 15 persons who work at a large assembly plant. The data are also in file XR09082. Assuming an approximately normal distribution of commuting times for those who work at the plant, construct and
9.81 Working independently, each of two researchers has devised a sampling plan to be carried out for the purpose of constructing a 90% confidence interval for the mean of a certain population. What is the probability that neither of their confidence intervals will include the population mean?
9.80 In a destructive test of product quality, a briefcase manufacturer places each of a simple random sample of the day’s production in a viselike device and measures how many pounds it takes to crush the case. From past experience, the standard deviation has been found to be 21.5 pounds. For 35
9.79 A quality-management supervisor believes that no more than 5% of the items in a recent shipment of 2000 are defective. If she wishes to determine, within 1 percentage point and with 99% confidence, the percentage of defective items in the shipment, how large a simple random sample would be
9.78 A university official wants to estimate, with 99%confidence and within $2, the average amount that members of fraternities and sororities spend at local restaurants during the first week of the semester. If the total fraternity/sorority membership is 300 people, how many members should be
9.77 A research firm supports a consumer panel of 2000 households that keep written diaries of their weekly grocery expenditures. The firm would like to estimate, with 95% confidence and within 4 percentage points, the percentage of its panel households who would be interested in providing more
9.76 A transportation company operates 200 trucks and would like to use a hidden speed monitor device to record the maximum speed at which a truck is operated during the period that the device is installed. The trucks are driven primarily on interstate highways, and the company wants to estimate
9.75 There are 100 members in the U.S. Senate. A political scientist wants to estimate, with 95% confidence and within 3 percentage points, the percentage who own stock in foreign companies. How many senators should be interviewed?Explain any assumptions you used in obtaining your recommended
9.74 A simple random sample is to be drawn from a population of 2000. The population standard deviation has been estimated as being 40 grams. In order to have 99%confidence that the sampling error in estimating is no more than 5 grams, what sample size will be necessary?
9.73 A simple random sample is to be drawn from a population of 800. In order to have 95% confidence that the sampling error in estimating is no more than 0.03, what sample size will be necessary?
9.72 A local environmental agency has selected a simple random sample of 16 homes to be tested for tap-water lead. Concentrations of lead were found to have a mean of 12 parts per billion and a standard deviation of 4 parts per billion. Con sidering that the homes were selected from a community in
9.71 Of 1200 undergraduates enrolled at a university, a simple random sample of 600 have been surveyed to measure student support for a $5 activities fee increase to help fund women’s intercollegiate athletics at the NCAA division 1A level. Of those who were polled, 55%supported the fee increase.
9.70 The personnel manager of a firm with 200 employees has selected a simple random sample of 40 employees and examined their health-benefit claims over the past year. The average amount claimed during the year was$260, with a standard deviation of $80. Construct and interpret the 95% confidence
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