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business statistics a first course

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

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 situations where the population is either infinite or very large compared to the sample size, what effect
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 this information only, what sample size was used?
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 conduct the study, will their maximum likely error be greater than, equal to, or less than 0.02? Why?
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 population proportion is believed to be no more than 0.15, how many owners must be included in a
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 Wheat for breakfast at least once last week. In determining the necessary size of a simple random sample
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 sample percentage will be within 3 percentage points of the actual population percentage, how large a
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 preliminary study, the population standard deviation has been estimated as 11.2 watts for these sets. In
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 to be undertaken, how large a simple random sample will be necessary to have 99% confidence that
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 machine’s output for the purpose of determining the average weight of product being packed by the machine.
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 making an interval estimate for a population mean, it is necessary to first make an estimate of the
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 questionnaire to a small simple random sampling of them. In one of the questions, the respondent is asked, “Do
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 codes and return problem categories are: (1) “doesn’t work,” (2) “excessive noise,” and(3)
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 800 union-member respondents, and 60%of them said they intended to vote for Ms. McCarthy.Based on the
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 interpret the 95% confidence interval for the population proportion of Americans who can name all
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 this age group, construct and interpret the 90% confidence interval for the population proportion of
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 the economic recession.Assuming this to be a simple random sample of U.S.adults, construct and
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 to vote for the new labor contract negotiated by union and management representatives.a. What is the
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% of all TV households. Assuming this estimate was based on a simple random sample of 1800 TV
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 that the survey included a simple random sample of 1200 companies, construct a 90% confidence interval
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 by persons in this age group, construct a 95% confidence interval for 5 the population proportion
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 $2000 worth of merchandise from the company during that year. Construct a 90%confidence interval
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 students to find out whether the student body thinks the school’s “Plundering Pirate” mascot should
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 travelers surveyed, 80 said e-mail access would be worth a slight extra cost. Construct a 95%
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. adults, construct a 95%confidence interval for 5 the population proportion of U.S. adults who
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 95% confidence interval for the population mean number of pairs of shoes owned by U.S. women. Based
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 interpret the 99%confidence interval for the population mean credit card debt for college juniors. Based
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 sample standard deviation of s 5 4.0 minutes, and from a population that is approximately normally
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 deviation of s 5 90 megabytes per month, construct and interpret the 95% confidence interval for the
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 random sample of 20 bottles of toner, the average was 1535 pages, with a standard deviation of 30
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 document with text and tables into a Microsoft Word file. The novices required an average time of 105
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 random sample of 16 fuses from its production output and found the amperages at which they
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 is approximately normally distributed, construct and interpret the 90% confidence interval for the
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 deviation were 25 minutes and 10 minutes, respectively.a. Construct and interpret the 95% confidence
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 ownership. The average number of defects was }x 5 3.7, with a standard deviation of 1.8 defects.a. Use the t
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 59 56 51 45 38 58 52 52 50 34 42 61 53 48 57 47 50 54
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 71 98 74 70 59 102 92 96
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 this indicate about the relationship between the t and standard normal distributions?
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 containers recently received from a long-time supplier. According to the supplier, the process by which the
“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 proportion of the population of employed adults who share this sentiment is between 0.419 and 0.481.”
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 constructing the confidence interval for the population mean?
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 Maryland bar exam, but only 60% passed. When asked about these results, the dean of this university’s
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 demanding industrial customer who insists on conducting a longevity test before committing to a
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 while person B (the “receiver”)tries to correctly identify the image person A is viewing.In carrying
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. According to the U.S. Census Bureau, the mean completion time for the long form is 38 minutes.
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 formulate policy for the community’s parks and recreation facilities. What is the probability that
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 customers, what is the probability that no more than 15 will be affected by the recall?
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. The students are surprised when they weigh the contents of their four packages and find the average
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. Assume that Charlie’s contacts represent a simple random sample of those who could have been called
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 consumer magazine purchase 40 of the clocks and find that the average clock in the sample deviated from
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, what assumption would be required if we are to use the standard normal distribution in determining
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 mean is to be just 5 grams?
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 sample mean is found to be }x 5 26.2 seconds per unit.a. What z-score corresponds to the sample mean
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 positively skewed, since persons who actually become customers require more of the caller’s time than
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 distribution.Source: hrblock.com, July 14, 2009.a. What additional assumption about 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 x.b. For the sample size n 5 2, determine the mean for each possible simple random sample from this
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 manager’s claim is correct, what is the probability that the sample proportion would be no more
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 a simple random sample of 300 voters, at least 60% would favor the candidate over her strongest
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. Determine the mean and the standard deviation of the 150 sample means, then compare these with their
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 standard deviation of the 150 sample means, then compare these with their theoretically expected values.
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 random sample of 40, 15% or more are defective. What is the probability that the shipment will be
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? Source: General Aviation Manufacturers Association, General Aviation Statistical Databook, 2008
A civic organization includes 200 members, who have an average income of $58,000, with a standard deviation of $10,000. A simple random sample of n 5 30 members is selected to participate in the annual fund-raising drive.What is the probability that the average income of the fund-raising group will
A population of 500 values is distributed such that 5 $1000 and 5 $400. For a simple random sample of n 5 200 values selected without replacement, describe the sampling distribution of the mean.
According to the Federal Trade Commission (FTC), about 3.4% of items come up at the wrong price when scanned at the retail checkout counter. Freda Thompson, director of investigations for her state’s consumer affairs office, sets up a study in which she has undercover shoppers (sometimes known as
8.29 The absentee rate for bus drivers in a large school district has been 5% in recent years. During the past few months, the school district and the bus drivers’ union have been engaged in negotiations for a new contract.Negotiations are at an impasse over several key issues, and the drivers
8.28 The Temployee Company supplies temporary workers to industry and has found that 58% of the positions it is asked to fill require a knowledge of Microsoft Excel. The firm currently has 25 individuals available who know Microsoft Excel. If Temployee Company receives 50 inquiries for temporary
8.27 A mail-order discount outlet for running shoes has found that 20% of the orders sent to new customers end up being returned for refund or exchange because of size or fit problems experienced by the customer. The 100-member Connor County Jogging Society has just found out about this mail-order
8.26 According to the Investment Company Institute, 40% of U.S. households have an Individual Retirement Account (IRA). Assuming the population proportion to be 5 0.40 and that a simple random sample of 400 households has been selected: Source: Investment Company Institute, 2008 Investment
8.25 It has been reported that 40% of U.S. workers employed as purchasing managers are females. In a simple random sample of U.S. purchasing managers, 70 out of the 200 are females. Given this information: Source: Bureau of the Census, Statistical Abstract of the United States 2009, p. 384.a. What
8.24 A simple random sample with n 5 200 is drawn from a bino mial process in which 5 0.6. Determine the following probabilities for p 5 the proportion of successes:a. P(0.50 # p)b. P(0.65 # p # 0.70)c. P(p $ 0.70)
8.23 A simple random sample with n 5 300 is drawn from a binomial process in which 5 0.4. Determine the following probabilities for p 5 the proportion of successes:a. P(p $ 0.35)b. P(0.38 # p # 0.42)c. P(p # 0.45)
8.22 Shirley Johnson, the county political leader discussed in Exercise 8.12, is a Republican. According to voter registration records, 60% of the homeowners in her county are also Republicans. For the simple random sample of 40 homeowners invited to attend her town meeting, describe the sampling
8.21 According to the Federal Reserve System, 46% of U.S. households have credit-card debt. For simple random samples of size n, with n . 30, describe the sampling distribution of p 5 the proportion of households in the sample who have credit-card debt. Source:Statistical Abstract of the United
8.20 According to the Newspaper Association of America, the average visitor to online newspaper sites spends 45 minutes per month reading online news content.Assuming a population standard deviation of 10 minutes and a simple random sample of 30 online newspaper readers, what is the probability
8.19 The average length of a hospital stay in general or community hospitals in the United States is 5.5 days.Assuming a population standard deviation of 2.5 days and a simple random sample of 50 patients, what is the probability that the average length of stay for this group of patients will be no
8.18 It has been reported that the average U.S. teenager sends 80 text messages per day. For purposes of this exercise, we will assume the daily number of text messages sent is normally distributed with a standard deviation of 15.0 messages. For a randomly selected group of 10 teenagers, and
8.17 At a department store catalog orders counter, the average time that a customer has to wait before being served has been found to be approximately exponentially distributed, with a mean (and standard deviation) of 3.5 minutes. For a simple random sample of 36 recent customers, invoke the
8.16 The tensile strength of spot welds produced by a robot welder is normally distributed, with a mean of 10,000 pounds per square inch and a standard deviation of 800 pounds per square inch. For a simple random sample of n 5 4 welds, what is the probability that the sample mean will be at least
8.15 A hardware store chain has just received a truckload of 5000 electric drills. Before accepting the shipment, the purchasing manager insists that 9 of the drills be randomly selected for testing. He intends to measure the maximum power consumption of each drill and reject the shipment if the
8.14 From past experience, an airline has found the luggage weight for individual air travelers on its trans- Atlantic route to have a mean of 80 pounds and a standard deviation of 20 pounds. The plane is consistently fully booked and holds 100 passengers. The pilot insists on loading an extra 500
8.13 An industrial crane is operated by four electric motors working together. For the crane to perform properly, the four motors have to generate a total of at least 380 horsepower. Engineers from the plant that produces the electric motors have stated that motors off their assembly line average
8.12 Shirley Johnson, a county political leader, is looking ahead to next year’s election campaign and the possibility that she might be forced to support a property tax increase to help combat projected shortfalls in the county budget. For the dual purpose of gaining voter support and finding
8.11 For the manufacturing plant discussed in Exercise 8.10, the union president and the human resources director jointly select a simple random sample of 36 employees to engage in a discussion with regard to the company’s work rules and overtime policies. What is the probability that the average
8.10 Employees in a large manufacturing plant worked an average of 62.0 hours of overtime last year, with a standard deviation of 15.0 hours. For a simple random sample of n 5 36 employees and x 5 the number of overtime hours worked last year, determine the z-score corresponding to each of the
For a random variable that is normally distributed, with 5 80 and 5 10, determine the probability that a simple random sample of 25 items will have a mean that isa. greater than 78.b. between 79 and 85.c. less than 85.
For a random variable that is normally distributed, with 5 200 and 5 20, determine the probability that a simple random sample of 4 items will have a mean that isa. greater than 210.b. between 190 and 230.c. less than 225.
A random variable is normally distributed with mean 5 $1500 and standard deviation 5 $100. Determine the standard error of the sampling distribution of the mean for simple random samples with the following sample sizes:a. n 5 16b. n 5 100c. n 5 400d. n 5 1000
The operator of a museum exhibit has found that 30%of the visitors donate the dollar that has been requested to help defray costs, with the others leaving without paying.Three visitors are on their way into the exhibit. Assuming that they will be making independent decisions on whether to donate
For a population of five individuals, television ownership is as follows:a. Determine the probability distribution for the discrete random variable, x 5 number of television sets owned. Calculate the population mean and standard deviation.b. For the sample size n 5 2, determine the mean for each
What is the difference between a standard deviation and a standard error?
Determine and interpret the value of the process capability index.
Construct and interpret statistical process control charts for variables and attributes.
Explain what is meant by statistical process control and describe how it contributes to the quality of manufactured products.
Describe, in general, how random and assignable process variation can each be identified and reduced.

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