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Introduction To Business Statistics 7th Edition Ronald M. Weiers - Solutions

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
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?
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 interpret
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 lb-ft.
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 episode of a network miniseries. How many television households must
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?In exerciseThere are approximately 113 million television households in the
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 to
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.
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 = 50, are to be drawn from the process, and a 90% confidence interval for the mean is to be
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 being
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. In exercise There
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
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
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 51
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.
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?
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
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?
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 interval for the population
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?
Seeing the fishing pole in his grandfather€™s office, Ted Thorndike€™s first thought is that old Luke is going to go fishing again and leave him to manage the store. He is quite surprised to learn the fishing pole is actually an inspiration for a new series of ads that Luke has in mind.The
The case in Chapter 2 listed 30 questions asked of 150 respondents in the community of Springdale. The coding key for the responses was also provided in that earlier exercise. The data are in file SHOPPING. In this exercise, some of the estimation techniques presented in the chapter will be applied
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?
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 student
A 1931 issue of Time magazine contained an advertisement for Liberty magazine. According to a study cited by Liberty, it was found that 15% of Liberty families had a “mechanical refrigerator,” compared to just 8% for all U.S. families. Assuming that the study included a sample of 120 Liberty
The administrator of a local hospital has told the governing board that 30% of its emergency room patients are not really in need of emergency treatment (i.e., the problems could just as easily have been handled by an appointment with their family physician). In checking a random sample of 400
In a taste comparison test, it was found that 58 of 100 persons preferred the chunky version of a peanut butter over the creamy type. An interested observer would like to determine whether this proportion (0.58) is significantly greater than the (0.50) proportion that would tend to result from
An exterminator claims that no more than 10% of the homes he treats have termite problems within 1 year after treatment. In a sample of 100 homes, local officials find that 14 had termites less than 1 year after being treated. At the 0.05 level of significance, evaluate the credibility of the
A national chain of health clubs says the mean amount of weight lost by members during the past month was at least 5 pounds. Skeptical of this claim, a consumer advocate believes the chain’s assertion is an exaggeration. She interviews a random sample of 40 members, finding their mean weight loss
In an interview with a local newspaper, a respected trial lawyer claims that he wins at least 75% of his court cases. Bert, a skeptical statistics student, sets up a one-tail test at the 0.05 level of significance to evaluate the attorney’s claim. The student plans to examine a random sample of
A consumer agency suspects that a pet food company may be under filling packages for one of its brands. The package label states “1600 grams net weight,” and the president of the company claims the average weight is at least 1600 grams. For a simple random sample of 35 boxes collected by the
Historically, Shop-Mart has gotten an average of 2000 hours of use from its G&E fluorescent lightbulbs. Because its fixtures are attached to the ceiling, the bulbs are rather cumbersome to replace, and Shop-Mart is looking into the possibility of switching to Phipps bulbs, which cost the same. A
Before installing a high-tech laser exhibit near the exit area, a museum of American technology found the average contribution by patrons was $2.75 per person. For a sample of 30 patrons following installation of the new exhibit, the contributions are as listed in data file XR10108. Based on the
According to the U.S. Department of Justice, 25% of violent crimes involve the use of a weapon. We will assume that data file XR10109 contains a sample of the crime information for a given city, with data for the 400 crimes coded as 1 = crime involved a weapon and 2 = crime did not involve a
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
Based on the sample results in Exercise 10.109, construct and interpret the 95% confidence interval for the population proportion. Is the hypothesized proportion (0.25) within the interval? Given the presence or absence of the 0.25 value within the interval, is this consistent with the findings of
In making aluminum castings into alternator housings, an average of 3.5 ounces per casting must be trimmed off and recycled as a raw material. A new manufacturing procedure has been proposed to reduce the amount of aluminum that must be recycled in this way. For a sample of 35 castings made with
Use the decision rule associated with Exercise 10.111 and a range of selected assumed values for μ to construct the power curve for the test. In exercise 10.111 In making aluminum castings into alternator housings, an average of 3.5 ounces per casting must be trimmed off and recycled as a raw
In the past, the mean lifetime of diesel engine injection pumps has been 12,000 operating hours. A new injection pump is available that is promoted as lasting longer than the old version. In a test of 50 of the new pumps, the lifetimes are as listed in data file XR10113. Based on the sample data,
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 to a. Never make a Type I error? b. Never make a Type II error? c. Compromise between Type I and Type II errors?
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 York,
In hypothesis testing, what is meant by the decision rule? What role does it play in the hypothesistesting procedure?
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: μ ≥ 3000 and H1: μ < 3000. For each of the following
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?
What is the central limit theorem, and how is it applicable to hypothesis testing?
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: μ ≥ 10, H1: μ < 10 b. H0: μ = 30, H1: μ ≠ 30 c. H0: μ > 90, H1: μ ≤ 90 d. H0: μ ≤ 75, H1:
What is a p-value, and how is it relevant to hypothesis testing?
For each of the following tests and z values, determine the p-value for the test:a. Right-tail test and z = 1.54b. Left-tail test and z = –1.03c. Two-tail test and z = –1.83
For each of the following tests and z values, determine the p-value for the test: a. Left-tail test and z = –1.62 b. Right-tail test and z = 1.43 c. Two-tail test and z = 1.27
For a sample of 35 items from a population for which the standard deviation is σ = 20.5, the sample mean is 458.0. At the 0.05 level of significance, test H0: μ = 450 versus H1: μ ≠ 450. Determine and interpret the p-value for the test.
For a sample of 12 items from a normally distributed population for which the standard deviation is σ = 17.0, the sample mean is 230.8. At the 0.05 level of significance, test H0: μ ≤ 220 versus H1: μ > 220. Determine and interpret the p-value for the test.
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 2.025
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: π ≥ 0.30, H1: π < 0.35 b. H0: π = 0.72, H1: π ≠ 0.72 c. H0: π ≤ 0.25, H1: π > 0.25 d. H0: π
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 expenditure for
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
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 to
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 for
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 XR10034.
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 α = 0.10 level: a. H0: μ = 170
Given the information in Exercise 10.27, construct a 95% confidence interval for the population mean, then reach a conclusion regarding whether μ could actually be equal to the value that has been hypothesized. How does this conclusion compare to that reached in Exercise 10.27? Why? In exercise
Given the information in Exercise 10.29, construct a 99% confidence interval for the population mean, then reach a conclusion regarding whether μ could actually be equal to the value that has been hypothesized. How does this conclusion compare to that reached in Exercise 10.29? Why? In exercise A
Use an appropriate confidence interval in reaching a conclusion regarding the problem situation and null hypothesis for Exercise 10.31. In exercise Following maintenance and calibration, an extrusion machine produces aluminum tubing with a mean outside diameter of 2.500 inches, with a standard
For a simple random sample of 40 items, x-bar = 25.9 and s = 4.2. At the 0.01 level of significance, test H0: μ = 24.0 versus H1: μ ≠ 24.0.
For a simple random sample of 15 items from a population that is approximately normally distributed, x-bar = 82.0 and s = 20.5. At the 0.05 level of significance, test H0: μ ≥ 90.0 versus H1: μ < 90.0.
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, can
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-bar = 479.6 miles and s = 42.8 miles, would this tend to cast doubt on the reported average of 464 miles? Use a
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 of 1.84 cups of coffee per day, with a standard deviation of 0.85 cups. In a two-tail test at the 0.05
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 received refunds last year, the mean amount was found to be $125, with a standard deviation of $43. Assuming
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 of membership to be 7.2 years, with a standard deviation of 2.5 years. Assuming the population is
A scrap metal dealer claims that the mean of his cash sales is “no more than $80,” but an Internal Revenue Service agent believes the dealer is untruthful. Observing a sample of 20 cash customers, the agent finds the mean purchase to be $91, with a standard deviation of $21. Assuming the
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 during that year, with a standard deviation of $210. Would a one-tail test at the 0.05 level suggest the
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 is obtained from a certain region of the United States and is found to have a mean net worth of $615,000,
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 the presence or absence of the $640,000 value within the interval, is this consistent with the findings
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 that the facility’s bulbs encounter might be having an adverse effect on the service life of bulbs in
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 working at the bank happens to be taking a statistics course and is curious as to whether the true average
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? Given the presence or absence of the 93 seconds value within the interval, is this consistent with the
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 persons is given the form, and their mean time to complete it is 36.8 minutes, with a standard deviation of
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? Given the presence or absence of the 38 minutes value within the interval, is this consistent with the
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 strategies to attract area teens to his mall, including live bands and “teenappreciation days” that
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 surveyed a simple random sample of 80 residents of her state, and that their auto insurance expenditures for
Using the sample data in Exercise 10.57, construct and interpret the 95% confidence interval for the population mean. Is the hypothesized population mean ($817) within the interval? Given the presence or absence of the $817 value within the interval, is this consistent with the findings of the
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
For a simple random sample, n = 200 and p = 0.34. At the 0.01 level, test H0: π = 0.40 versus H1: ≠ 0.40.
For a simple random sample, n = 1000 and p = 0.47. At the 0.05 level, test H0: π ≥ 0.50 versus H1: π < 0.50.
For a simple random sample, n = 700 and p = 0.63. At the 0.025 level, test H0: π ≤ 0.60 versus H1: π > 0.60.
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 the shipment are defective. Carry out an appropriate hypothesis test and comment on the credibility of the
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 materials were sent, 30 students applied for admission. In a two-tail test at the 0.05 level of
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 agreement specified that random urine checks could be carried out to ascertain compliance. In a random
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 the 0.05 level of significance, can we conclude that the percentage who prefer electric heating may differ
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 improved the likelihood of an individual’s passing on his or her first try. In a sample of 250 recent
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 have purchased life insurance. At the 0.05 level in a one-tail test, is this sample finding significantly
According to the National Association of Home Builders, 55% of new single-family homes built during 2005 had a fireplace. Suppose a nationwide homebuilder has claimed that its homes are “a cross section of America,” but a simple random sample of 600 of its single-family homes built during that
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
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 the presence or absence of the 0.55 value within the interval, is this consistent with the findings of
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. A prominent politician is interested in how young working women within her county compare to this national percentage, and selects a simple random sample
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 interval? Given the presence or absence of the 0.07 value within the interval, is this consistent with the
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 Brad, consumers claim to like the brand-name products better than the generics, but they can’t even tell
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 of the ways the IRS oversees its auditors is to monitor the percentage of cases that result in the taxpayer
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 the presence or absence of the 0.80 value within the interval, is this consistent with the findings of
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 student body as a whole. Assume that data file XR10076 shows the current status for a sample of 200 male

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