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Business Statistics In Practice 6th Edition Bruce Bowerman, Richard O'Connell - Solutions
An advertising agency conducted an ad campaign aimed at making consumers in an Eastern state aware of a new product. Upon completion of the campaign, the agency claimed that 20 percent of consumers in the state had become aware of the product. The product's distributor surveyed 1,000 consumers in
In order to gain additional information about respondents, some marketing researchers have used ultraviolet ink to precode questionnaires that promise confidentiality to respondents. Of 205 randomly selected marketing researchers who participated in an actual survey, 117 said that they disapprove
When a store uses electronic article surveillance (EAS) to combat shoplifting, it places a small sensor on each item of merchandise. When an item is legitimately purchased, the sales clerk is supposed to remove the sensor to prevent an alarm from sounding as the customer exits the store. In an
A department store will place a sale item in a special display for a one-day sale. Previous experience suggests that 20 percent of all customers who pass such a special display will purchase the item. If 2,000 customers will pass the display on the day of the sale, and if a one-item-per-customer
Suppose that the random variable x has an exponential distribution with A = 2.a. Write the formula for the exponential probability curve of x. What are the possible values of x?b. Sketch the probability curve.c. Find P(x < 1).d. Find P(.25 ≤ x ≤ 1).e. Find P(x ≥ 2).f. Calculate the mean,
Repeat Exercise 6.54 with A = 3.Suppose that the random variable x has an exponential distribution with A = 2.a. Write the formula for the exponential probability curve of x. What are the possible values of x?b. Sketch the probability curve.c. Find P(x < 1).d. Find P(.25 ≤ x ≤ 1).e. Find P(x
Recall in Exercise 5.34 (page 222) that the number of customer arrivals at a bank's drive-up window in a 15-minute period is Poisson distributed with a mean of seven customer arrivals per 15-minute period. Define the random variable x to be the time (in minutes) between successive customer arrivals
The length of a particular telemarketing phone call, x, has an exponential distribution with mean equal to 1.5 minutes.a. Write the formula for the exponential probability curve of x.b Sketch the probability curve of x.c. Find the probability that the length of a randomly selected call will be(1)
The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of two breakdowns every 500 hours. Let x denote the time (in hours) between successive breakdowns.a. Find A and μx.b. Write the formula for the
Suppose that the number of accidents occurring in an industrial plant is described by a Poisson distribution with an average of one accident per month. Let x denote the time (in months) between successive accidents.a. Find the probability that the time between successive accidents is(1) More than
Suppose that the random variable x has a uniform distribution with c = 2 and d = 8.a. Write the formula for the probability curve of x, and write an interval that gives the possible values of x.b. Graph the probability curve of x.c. Find P (3 ≤ x ≤ 5).d. Find P (1.5 ≤ x ≤ 6.5).e. Calculate
Discuss how a normal probability plot is constructed.
Consider the sample of 12 incomes given in Example 3.2 (page 105). a. Sort the income data from smallest to largest, and compute i/(n + 1) for each observation. b. Compute the standardized normal quantile value O, for each observation. c. Graph the normal probability plot for the salary data and
Consider the 20 DVD satisfaction ratings given on page 123. Construct a normal probability plot for these data and interpret the plot.
A normal probability plot can be constructed using MINITAB. Use the selections Stat: Basic Statistics Normality test, and select the data to be analyzed. Although the MINITAB plot is slightly different from the plot outlined in this section, its interpretation is the same. Use MINITAB to construct
In a murder trial in Los Angeles, a shoe expert stated that the range of heights of men with a size 12 shoe is 71 inches to 76 inches. Suppose the heights of all men wearing size 12 shoes are normally distributed with a mean of 73.5 inches and a Standard deviation of 1 inch. What is the probability
In the movie Forrest Gump, the public school required an IQ of at least 80 for admittance.a. If IQ test scores are normally distributed with mean 100 and standard deviation 16, what percentage of people would qualify for admittance to the school?b. If the public school wishes 95 percent of all
The amount of sales tax paid on a purchase is rounded to the nearest cent. Assume that the roundoff error is uniformly distributed in the interval -.5 to .5 cents. a. Write the formula for the probability curve describing the round-off error. b. Graph the probability curve describing the round-off
A consensus forecast is the average of a large number of individual analysts' forecasts. Suppose the individual forecasts for a particular interest rate are normally distributed with a mean of 5.0 percent and a standard deviation of 1.2 percent. A single analyst is randomly selected. Find the
Recall from Exercise 6.69 that individual forecasts of a particular interest rate are normally distributed with a mean of 5 percent and a standard deviation of 1.2 percent. a. What percentage of individual forecasts are at or below the 10th percentile of the distribution of forecasts? What
The scores on the entrance exam at a well-known, exclusive law school are normally distributed with a mean score of 200 and a standard deviation equal to 50. At what value should the lowest passing score be set if the school wishes only 2.5 percent of those taking the test to pass?
A machine is used to cut a metal automobile part to its desired length. The machine can be set so that the mean length of the part will be any value that is desired. The standard deviation of the lengths always runs at .02 inches. Where should the mean be set if we want only .4 percent of the parts
Suppose a software company finds that the number of errors in its software per 1,000 lines of code is described by a Poisson distribution. Furthermore, it is found that there is an average of four errors per 1,000 lines of code. Letting x denote the number of lines of code between successive
For each investment class in Table 3.11 (page 143), assume that future returns are normally distributed with the population mean and standard deviation given in Table 3.11. Based on this assumption: a. For each investment class, find the probability of a return that is less than zero (that is, find
Net interest margin-often referred to as spread-is the difference between the rate banks pay on deposits and the rate they charge for loans. Suppose that the net interest margins for all U.S. banks are normally distributed with a mean of 4.15 percent and a standard deviation of .5 percent. a. Find
Assume that the waiting time X for an elevator is uniformly distributed between zero and six minutes.a. Write the formula for the probability curve of x.b. Graph the probability curve of x.c. Find P(2 ≤ x ≤ 4).d. Find P (3 ≤ x ≤ 6).e. Find P({0 ≤ x ≤ 2} or {5 ≤ x ≤ 6}).
In an article in the November II. 1991. issue of Advertising Age, Nancy Giges studies global spending patterns. Giges presents data concerning the percentage of adults in various countries who have purchased various consumer items (such as soft drinks, athletic footware. blue jeans, beer, and so
Refer to Exercise 6.8. a. Calculate the mean. μx, the variance, σx and the standard deviation, σx. b. Find the probability that the waiting time of a randomly selected patron will be within one standard deviation of the mean.
Discuss how we select a random sample.
For each situation in Exercise 7.9, find an interval that contains (approximately or exactly) 99.73 percent of all the possible sample means. In which cases must we assume that the population is normally distributed? Why?a. μ = 10, σ = 2, n = 25b. μ = 500, σ = .5, n = 100c. μ = 3, σ = .1, n =
Suppose that we will randomly select a sample of 64 measurements from a population having a mean equal to 20 and a standard deviation equal to 4.a. Describe the shape of the sampling distribution of the sample mean . Do we need to make am assumptions about the shape of the population? Why or why
Find the probability distribution of the population of six sample mean grand prizes.This question is based on the situation below.Congratulations! You have just won the question-and-answer portion of a popular game show and will now be given an opportunity to select a grand prize. The game show
Compare the probability distribution of the four individual grand prizes with the probability distribution of the six sample mean grand prizes. Would you select one or two envelopes? Why? Note: There is no one correct answer. It is a matter of opinion. This question is based on the situation
Recall that the bank manager wants to show that the new system reduces typical customer waiting times to less than six minutes. One way to do this is to demonstrate that the mean of the population of all customer waiting times is less than 6. Letting this mean be μx, in this exercise we wish to
Recall that a customer is considered to be very satisfied with his or her XYZ Box video game system if the customer's composite score on the survey instrument is at least 42. One way to show that customers are typically very satisfied is to show that the mean of the population of all satisfaction
In an article in the Journal of Management, Joseph Martocchio studied and estimated the costs of employee absences. Based on a sample of 176 blue-collar workers, Martocchio estimated that the mean amount of paid time lost during a three-month period was 1.4 days per employee with a standard
Explain why sampling without replacement is preferred to sampling with replacement.
When a pizza restaurant's delivery process is operating effectively, pizzas are delivered in an average of 45 minutes with a standard deviation of 6 minutes. To monitor its delivery process, the restaurant randomly selects five pizzas each night and records their delivery times. a. For the sake of
In each of the following cases, determine whether the sample size n is large enough to say that the sampling distribution of p is a normal distribution. a. p = .4. n = 100 b. p = .1. n = 10 c. p = .1, n = 50 d. p = .8, n = 400 e. p = .98. n = 1.000 f. p = .99, n = 400
In each of the following cases, find the mean, variance, and standard deviation of the sampling distribution of the sample proportion p. a. p = .5, n = 250 b. p = .1. n = 100 c. p = .8. n = 400 d. p = .98, n = 1,000
For each situation in Exercise 7.25, find an interval that contains approximately 95.44 percent of all the possible sample proportions. a. p = .5, n = 250 b. p = .1. n = 100 c. p = .8. n = 400 d. p = .98, n = 1,000
Suppose that we will randomly select a sample of n = 100 elements from a population and that we will compute the sample proportion of these elements that fall into a category of interest. If the true population proportion p equals .9:a. Describe the shape of the sampling distribution of . Why
For the situation in Exercise 7.27. calculate the following probabilities. In each case sketch the sampling distribution and the probability.1. P( > .96)2. P(855 ≤ p ≤ .945)3. P(p ≤ .915)
In the July 29, 2001, issue of The Journal News (Hamilton, Ohio) Lynn Elber of the Associated Press reported on a study conducted by the Kaiser Family Foundation regarding parents' use of television set V-chips for controlling their childrens' TV viewing. The study asked parents who own TVs
On February 8, 2002, the Gallup Organization released the results of a poll concerning American attitudes toward the 19th Winter Olympic Games in Salt Lake City, Utah. The poll results were based on telephone interviews with a randomly selected national sample of 1,011 adults. 18 years and older,
Quality Progress, February 2005, reports on improvements in customer satisfaction and loyalty made by Bank of America. A key measure of customer satisfaction is the response (on a scale from I to 10) to the question: "Considering all the business you do with Bank of America, what is your overall
Again consider the survey of 350 Bank of America customers discussed in Exercise 7.31. and assume that 48% of Bank of America customers would currently express customer delight. That is. assume p = .48. Find: a. The probability that the sample proportion obtained from the sample of 350 Bank of
Based on your results in Exercise 7.32, would it be reasonable to state that the survey's "margin of error" is ± 3 percentage points? ± 6 percentage points? Explain. a. The probability that the sample proportion obtained from the sample of 350 Bank of America customers would be within three
A special advertising section in the July 20, 1998, issue of Fortune magazine discusses "outsourcing." According to the article, outsourcing is "the assignment of critical, but noncore, business functions to outside specialists." This allows a company to immediately bring operations up to
The July 20, 1998, issue of Fortune magazine reported the results of a survey on executive training that was conducted by the Association of Executive Search Consultants. The survey showed that 75 percent of 300 polled CEOs believe that companies should have "fast-track training programs"" for
When is it appropriate to use stratified random sampling? What are strata, and how should strata be selected?
Explain how to take a systematic sample of 100 companies from the 1,853 companies that are members of an industry trade association. Discuss.
Explain how a stratified random sample is selected. Discuss how you might define the strata to survey student opinion on a proposal to charge all students a $100 fee for a new university-run bus system that will provide transportation between off-campus apartments and campus locations.
A company that produces and markets video game systems wishes to assess its customer's level of satisfaction with a relatively new model, the XYZ-Box. In the six months since the introduction of the model, the company has received 73,219 warranty registrations from purchasers. The company will
Explain each of the following terms: a. Undercoverage b. Nonresponse c. Response bias
Each day a manufacturing plant receives a large shipment of drums of Chemical ZX-900. These drums are supposed to have a mean fill of 50 gallons, while the fills have a standard deviation known to be .6 gallon. a. Suppose that the mean fill for the shipment is actually 50 gallons. If we draw a
In its October 12, 1992. issue. The Milwaukee Journal published the results of an Ogilvy, Adams, and Rinehart poll of 1,250 American investors that was conducted in early October 1992. The poll investigated the stock market's appeal to investors five years after the market suffered its biggest
Again consider the stock market poll discussed in Exercise 7.47. a. Suppose we wish to use the poll's results to justify the claim that fewer than 50 percent of American investors in 1992 found the stock market less attractive than in 1987. The poll actually found that 41 percent of the respondents
Aamco Heating and Cooling, Inc., advertises that any customer buying an air conditioner during the first 16 days of July will receive a 25 percent discount if the average high temperature for this 16-day period is more than five degrees above normal. a. If daily high temperatures in July are
Recall that the trash bag manufacturer has concluded that its new 30-gallon bag will be the strongest such bag on the market if its mean breaking strength is at least 50 pounds. In order to provide statistical evidence that the mean breaking strength of the new bag is at least 50 pounds, the
Suppose that we wish to assess whether more than 60 percent of all United Kingdom households spent on life insurance in 1993. That is, we wish to assess whether the proportion, p, of all United Kingdom households that spent on life insurance in 1993 exceeds .60. Assume here that the U.K. insurance
The best way to observe, first-hand, the concepts of sampling distributions is to conduct sampling experiments with real data. However, sampling experiments can be prohibitively time consuming and tedious. An excellent alternative is to conduct computer-assisted sampling experiments or simulations.
In an article entitled "Turned Off in the June 2-4, 1995, issue of USA Weekend, Don Olmsted and Gigi Anders reported results of a survey where readers were invited to write in and express their opinions about sex and violence on television. The results showed that 96 percent of respondents were
Suppose that we will take a random sample of size n from population having mean fx and standard deviation a. For each of the following situations, find the mean, variance, and standard deviation of the sampling distribution of the sample mean x: a. μ = 10, σ = 2, n = 25 b. μ = 500, σ = .5, n =
In an article in Marketing Science, Silk and Berndt investigate the output of advertising agencies. They describe ad agency output by finding the shares of dollar billing volume coming from various media categories such as network television, spot television, newspapers, radio, and so forth. a.
In an article in Accounting and Business Research, Carslaw and Kaplan investigate factors that influence "audit delay" for firms in New Zealand. Audit delay, which is defined to be the length of time (in days) from a company's financial year-end to the date of the auditor's report, has been found
In an article in the Journal of Marketing, Bayus studied the differences between "early replacement buyers" and "late replacement buyers" in making consumer durable good replacement purchases. Early replacement buyers are consumers who replace a product during the early part of its lifetime, while
Suppose that for a sample of n = 11 measurements, we find that n = 72 and s = 5. Assuming normality, compute confidence intervals for the population mean μ with the following levels of confidence: a. 95% b. 99% c. 80% d. 90% e. 98% f. 99.8%
The bad debt ratio for a financial institution is defined to be the dollar value of loans defaulted divided by the total dollar value of all loans made. Suppose a random sample of seven Ohio banks is selected and that the bad debt ratios (written as percentages) for these banks are 7 percent, 4
In an article in Quality Progress, Blauw and During study how long it takes Dutch companies to complete five stages in the adoption of total quality control (TQC). According to Blauw and During, the adoption of TQC can be divided into five stages as follows: 1. Knowledge: the organization has heard
The mean and the standard deviation of the sample of 40 trash bag breaking strengths in Table 1.9 are x̅ = 50.575 and s = 1.6438. Calculate a t-based 95 percent confidence interval for μ, the mean of the breaking strengths of all possible trash bags of the new type. Also, find this interval using
Consider a population having a standard deviation equal to 10. We wish to estimate the mean of this population.a. How large a random sample is needed to construct a 95 percent confidence interval for the mean of this population with a margin of error equal to 1?b. Suppose that we now take a random
a. What does a population proportion tell us about the population?b. Explain the difference between p and p.c. What is meant when a public opinion poll's margin of error is 3 percent?
In each of the following cases, determine whether the sample size n is large enough to use the large sample formula presented in the box on page 329 to compute a confidence interval for p.a. p̂ = .1, n = 30b. p̂ = .1, n = 100c. p̂ = .5, n = 50d. p̂ = .8, n = 400e. p̂ = .9, n = 30f. p̂ = .99,
In each of the following cases, compute 95 percent, 98 percent, and 99 percent confidence intervals for the population proportion p.a. p̂ = .4 and n = 100 b. p̂ = .1 and n = 300 c. p̂ = .9 and n = 100d. p̂ = .6 and n = 50
Quality Progress, February 2005, reports on the results achieved by Bank of America in improving customer satisfaction and customer loyalty by listening to the 'voice of the customer.' A key measure of customer satisfaction is the response on a scale from 1 to 10 to the question: "Considering all
On January 7, 2000, the Gallup Organization released the results of a poll comparing the lifestyles of today with yesteryear. The survey results were based on telephone interviews with a randomly selected national sample of 1,031 adults, 18 years and older, conducted December 20-21, 1999.4 a. The
In an article in the Journal of Advertising, Weinberger and Spotts compare the use of humor in television ads in the United States and the United Kingdom. They found that a substantially greater percentage of U.K. ads use humor. a. Suppose that a random sample of 400 television ads in the United
The manufacturer of the ColorSmart-5000 television set claims 95 percent of its sets last at least five years without needing a single repair. In order to test this claim, a consumer group randomly selects 400 consumers who have owned a ColorSmart-5000 television set for five years. Of these 400
In the book Cases in Finance, Nunnally and Plath present a case in which the estimated percentage of uncollectible accounts varies with the age of the account. Here the age of an unpaid account is the number of days elapsed since the invoice date. Suppose an accountant believes the percentage of
Referring to Exercise 8.46. determine the sample size needed in order to be 99 percent confident that , the sample proportion of ColorSmart-5000 television sets that last at least five years without a single repair, is within a margin of error of .03 of p, the true proportion of sets that last at
A retailer that sells home entertainment systems accumulated 10,451 sales invoices during the previous year. The total of the sales amounts listed on these invoices (that is, the total sales claimed by the company) is $6,384,675. In order to estimate the true total sales for last year, an
A company's manager is considering simplification of a travel voucher form. In order to assess the costs associated with erroneous travel vouchers, the manager must estimate the total number of such vouchers that were filled out incorrectly in the last month. In a random sample of 100 vouchers
A personnel manager is estimating the total number of person-days lost to unexcused absences by hourly workers in the last year. In a random sample of 50 employees drawn without replacement from the 687 hourly workers at the company, records show that the 50 sampled workers had an average of =
An auditor randomly samples 32 accounts receivable without replacement from a firm's 600 accounts and checks to verify that all documents for the accounts comply with company procedures. Ten of the 32 accounts are found to have documents not in compliance. Find a point estimate of and a 95 percent
a. Estimating p and гConsider randomly selecting a sample of n measurements without replacement from a finite population consisting of N measurements and having variance σ2. Also consider the sample size given by the formulaThen, it can be shown that this sample size makes the margin of error
Suppose that, for a sample of size n = KK) measurements, we find that x = 50. Assuming that IT equals 2, calculate confidence intervals for the population mean /x with the following confidence levels: a. 959 b 99% c. 97% d. 80% e. 99.73% f. 92%
The mean and the standard deviation of the sample of 40 trash bag breaking strengths are = 50.575 and s = l .6438. We give the mean and the standard deviation of a sample that has been randomly selected from a population. For each exercise, find estimated tolerance intervals that contain
The mean and the standard deviation of the sample of 100 bank customer waiting times are = 5.46 and s = 2.475.We give the mean and the standard deviation of a sample that has been randomly selected from a population. For each exercise, find estimated tolerance intervals that contain approximately
The mean and the standard deviation of the sample of 65 customer satisfaction ratings are = 42.95 and s = 2.6424.We give the mean and the standard deviation of a sample that has been randomly selected from a population. For each exercise, find estimated tolerance intervals that contain
In an article in the Journal of Accounting Research, Ashton, Willingham. and Elliott studied audit delay (the length of time from a company's fiscal year-end to the date of the auditor's report) for industrial and financial companies. In the study, a random sample of 250 industrial companies
In an article in Accounting and Business Research, Beattie and Jones investigate the use and abuse of graphic presentations in the annual reports of United Kingdom firms. The authors found that 65 percent of the sampled companies graph at least one key financial variable, but that 30 percent of the
On January 4. 2000, the Gallup Organization released the results of a poll dealing with the likelihood of computer-related Y2K problems and the possibility of terrorist attacks during the New Year's holiday at the turn of the century.7 The survey results were based on telephone interviews with a
The manager of a chain of discount department stores wishes to estimate the total number of erroneous discounts allowed by sales clerks during the last month. A random sample of 200 of the chain's 57.532 transactions for the last month reveals that erroneous discounts were allowed on eight of the
National Motors has equipped the ZX-900 with a new disk brake system. We define the stopping distance for a ZX-900 to be the distance (in feet) required to bring the automobile to a complete stop from a speed of 35 mph under normal driving conditions using this new brake system. In addition, we
A large construction contractor is building 257 homes, which are in various stages of completion. For tax purposes, the contractor needs to estimate the total dollar value of its inventory due to construction in progress. The contractor randomly selects (without replacement) a sample of 40 of the
Consider the trash bag problem. Suppose that an independent laboratory has tested trash bags and has found that no 30-gallon bags that are currently on the market have a mean breaking strength of 50 pounds or more. On the basis of these results, the producer of the new, improved trash bag feels
In an article in the Journal of Retailing, J. G. Blodgett, D. H. Granbois, and R. G. Walters investigated negative word-of-mouth consumer behavior. In a random sample of 201 consumers, 150 reported that they engaged in negative word-of-mouth behavior (for instance, they vowed never to patronize a
In an article in the Journal of Management Information Systems, Mahmood and Mann investigate how information technology (IT) investment relates to company performance. In particular, Mahmood and Mann obtain sample data concerning IT investment for companies that use information systems effectively.
Suppose that random samples of 50 returns for each of the following investment classes give the indicated sample mean and sample standard deviation: Fixed annuities: = 7.83%, s = .51% Domestic large cap stocks: = 13.42%, s = 15.17% Domestic midcap stocks: = 15.03%, s = 18.44% Domestic small cap
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