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business
business statistics a first course

Questions and Answers of Business Statistics A First Course

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
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
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
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
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
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
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
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
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%
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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%
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
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
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
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
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
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
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
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
9.68 As a rule of thumb, under what conditions should the finite population correction be employed in determining confidence intervals and calculating required sample sizes?9.69 Compared to
9.67 In reporting the results of their survey of a simple random sample of U.S. registered voters, pollsters claim 95% confidence that their sampling error is no more than 4 percentage points. Given
9.66 In Exercise 9.65, suppose that (unknown to the dealers) the actual population proportion is really 0.35.If they use their estimated value ( # 0.15) in determining the sample size and then
9.65 The Chevrolet dealers of a large county are conducting a study to determine the proportion of car owners in the county who are considering the purchase of a new car within the next year. If the
9.64 Suppose that Nabisco would like to determine, with 95% confidence and a maximum likely error of 0.03, the proportion of first graders in Pennsylvania who had Nabisco’s Spoon-Size Shredded
9.63 A national political candidate has commissioned a study to determine the percentage of registered voters who intend to vote for him in the upcoming election. To have 95% confidence that the
9.62 A consumer agency has retained an independent testing firm to examine a television manufacturer’s claim that its 50-inch console model consumes just 110 watts of electricity. Based on a
9.61 Based on a pilot study, the population standard deviation of scores for U.S. high school graduates taking a new version of an aptitude test has been estimated as 3.7 points. If a larger study is
9.60 From past experience, a package-filling machine has been found to have a process standard deviation of 0.65 ounces of product weight. A simple random sample is to be selected from the
9.58 “If we want to cut the maximum likely error in half, we’ll have to double the sample size.” Is this statement correct? Why or why not?9.59 In determining the necessary sample size in
9.57 An investment counselor has purchased a large mailing list consisting of 50,000 potential investors. Before creating a brochure to send to members of the list, the counselor mails a
9.56 In the documentation that accompanies its products that are returned for in-warranty service, a manufacturer of electric can openers asks the customer to indicate the reason for the return. The
9.55 Estelle McCarthy, a candidate for state office in New Jersey, has been advised that she must get at least 65% of the union vote in her state. A recent political poll of likely voters included
9.54 A Zogby poll found that 75% of Americans can name all of The Three Stooges—Moe, Curly, and Larry. Assuming this finding to be based on a simple random sample of 1200 Americans, construct and
9.53 According to a National Organization for Youth Safety Survey of 605 drivers aged 16–20, 68% have sent a text message while driving. Assuming this to be a simple random sample of drivers from
9.52 A 2009 Pew Internet & American Life Project survey of 2253 U.S. adults found that 69% were using the Internet to help them find jobs, bargains, benefits, financing, and to otherwise cope with
Repeat Exercise 9.50, but assume that the sample size was n 5 900 instead of n 5 100.
In a major industry where well over 100,000 manufacturing employees are represented by a single union, a simple random sampling of n 5 100 union members finds that 57% of those in the sample intend
According to Nielsen Media Research viewership data, the top television broadcast of all time was the last episode of M*A*S*H, which aired on February 28, 1983, and was viewed by an estimated 60.2%
A study by Careerbuilder.com found that 20% of companies check out job candidates’ profiles on social networking sites like Facebook and MySpace before deciding whether to employ them. Assuming
It has been estimated that 48% of U.S. households headed by persons in the 35– 44 age group own mutual funds. Assuming this finding to be based on a simple random sample of 1000 households headed
In examining a simple random sample of 100 sales invoices from several thousand such invoices for the previous year, a researcher finds that 65 of the invoices involved customers who bought less than
In response to media inquiries and concerns expressed by groups opposed to violence, the president of a university with over 25,000 students has agreed to survey a simple random sample of her
An airline has surveyed a simple random sample of air travelers to find out whether they would be interested in paying a higher fare in order to have access to e-mail during their flight. Of the 400
A pharmaceutical company found that 46% of 1000 U.S. adults surveyed knew neither their blood pressure nor their cholesterol level. Assuming the persons surveyed to be a simple random sample of U.S.
According to a Kelton Research survey, the average U.S. woman owns 15 pairs of shoes. Under the assumption that this finding was based on the sample data in file XR09041, construct and interpret the
Sallie Mae researchers report that the average college junior has a credit card debt of $2912. Under the assumption that this finding was based on the sample data in file XR09040, construct and
According to Nielsen/NetRatings, the average visitor to amazon.com spends 19.7 minutes at the site.Assuming this finding to be based on a simple random sample of 20 visitors to the site, with a
The average capacity usage for iPhone users has been estimated as 400 megabytes per month. Assuming this finding to be based on a simple random sample of 80 iPhone users, with a sample standard
An office equipment manufacturer has developed a new photocopy machine and would like to estimate the average number of 81/2-by-11 copies that can be made using a single bottle of toner. For a simple
The author of an entry-level book on using Microsoft Word has carried out a test in which 35 novices were provided with the book, a computer, and the assignment of converting a complex handwritten
One of the most popular products sold by a manufacturer of electrical fuses is the standard 30-ampere fuse used by electrical contractors in the construction industry. The company has tested a simple
An automobile rental agency has the following mileages (in thousands) for a simple random sample of 20 cars rented last year. Given this information, and assuming the data are from a population that
The service manager of Appliance Universe has recorded the times for a simple random sample of 50 refrigerator service calls taken from last year’s service records. The sample mean and standard
A consumer magazine has contacted a simple random sample of 33 owners of a certain model of automobile and asked each owner how many defects had to be corrected within the first 2 months of
Given the following observations in a simple random sample from a population that is approximately normally distributed, construct and interpret the 95%and 99% confidence intervals for the mean:66 34
Given the following observations in a simple random sample from a population that is approximately normally distributed, construct and interpret the 90%and 95% confidence intervals for the mean:67 79
For df 5 85, determine the value of A that corresponds to each of the following probabilities:a. P(t $ A) 5 0.10b. P(t # A) 5 0.025c. P(2A # t # A) 5 0.98
For df 5 25, determine the value of A that corresponds to each of the following probabilities:a. P(t $ A) 5 0.025b. P(t # A) 5 0.10c. P(2A # t # A) 5 0.99
Why are the t values listed in the df 5 infinity row of the t distribution table identical to the z values that correspond to the same right-tail areas of the standard normal distribution? What does
Sheila Johnson, a state procurement manager, is responsible for monitoring the integrity of a wide range of products purchased by state agencies. She is currently examining a sample of paint
“In surveying a simple random sample of 1000 employed adults, we found that 450 individuals felt they were underpaid by at least $3000. Based on these results, we have 95% confidence that the
A population is approximately normally distributed and the sample size is to be n 5 40. What additional factor must be considered in determining whether to use the standard normal distribution in
Differentiate between a point estimate and an interval estimate for a population parameter.
The overall pass rate for law school graduates taking the Maryland bar exam has been reported as 76%. Assume that a certain Maryland law school has had 400 of its most recent graduates take the
A lighting vendor has described its incandescent bulbs as having normally distributed lifetimes with a mean of 2000 hours and a standard deviation of 100 hours. The vendor is faced with an especially
In performing research on extrasensory perception, researchers sometimes place two individuals in different locations, then have person A (the “sender”) view each item in a series of stimuli
8.55 In the 2000 census, the so-called “long form”received by one of every six households contained 52 questions, ranging from your occupation and income all the way to whether you had a bathtub.
8.54 Seventy percent of the registered voters in a large community are Democrats. The mayor will be selecting a simple random sample of 20 registered voters to serve on an advisory panel that helps
8.53 Of 500 vehicles sold by an auto dealership last month, 200 have a defect that will require a factory recall for dealer correction. For a simple random sample of n 5 50 of last month’s
8.52 As a project for their high school mathematics class, four class members purchase packages of a leading breakfast cereal for subsequent weighing and comparison with the 12-ounce label weight.
8.51 Based on past experience, 20% of the contacts made by a firm’s sales representatives result in a sale being made. Charlie has contacted 100 potential customers but has made only 10 sales.
8.50 The manufacturer of a travel alarm clock claims that, on the average, its clocks deviate from perfect time by 30 seconds per month, with a standard deviation of 10 seconds. Engineers from a
8.49 Employees at a corporate headquarters own an average of 240 shares of the company’s common stock, with a standard deviation of 40 shares. For a simple random sample consisting of 5 employees,
8.48 For a given sample size, the standard error of the sample mean is 10 grams. With other factors unchanged, to what extent must the sample size be increased if the standard error of the sample
8.47 When a production machine is properly calibrated, it requires an average of 25 seconds per unit produced, with a standard deviation of 3 seconds. For a simple random sample of n 5 36 units, the
8.46 Based on past experience, a telemarketing firm has found that calls to prospective customers take an average of 2.0 minutes, with a standard deviation of 1.5 minutes.The distribution is
8.45 In 2009, the average fee paid by H&R Block tax preparation customers was $187. Assume that the standard deviation of fees was $60 but that we have no idea regarding the shape of the population
8.44 Given the following probability distribution for an infinite population with the discrete random variable, x:x 0 1 2 3 P(x) 0.2 0.1 0.3 0.4a. Determine the mean and the standard deviation of
8.43 For the situation described in Exercise 8.42, suppose that only 49% of the registered voters in the sample favor the candidate over her strongest opponent. Given this result:a. If the campaign
The campaign manager for a political candidate claims that 55% of registered voters favor the candidate over her strongest opponent. Assuming that this claim is true, what is the probability that in
Repeat Exercise 8.40, but with n 5 30 observations in each sample.
Using the procedures in Computer Solutions 8.1 as a general guide, simulate 150 simple random samples of size n 5 4 from a normal distribution with a mean of 80 and a standard deviation of 20.
Repeat Exercise 8.38, but with n 5 30 observations in each sample.
Using the procedures in Computer Solutions 8.1 as a general guide, simulate 150 simple random samples of size n 5 2 from an exponential distribution with a mean of 6. Determine the mean and the
A firm’s receiving department has just taken in a shipment of 300 generators, 20% of which are defective.The quality control inspector has been instructed to reject the shipment if, in a simple
Of the 217 airports available for public use in Belgium, 132 are paved. For a simple random sample of n 5 50, what is the probability that at least 22 of the airports in the sample will be paved?

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