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Essentials Of Business Statistics 5th Edition Bruce Bowerman, Richard Connell, Emily Murphree, Burdeane Or - Solutions

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? In Exercise 7.9 Suppose that we will take a random sample of size n from a
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 any assumptions about the shape of the population? Why or why
Find the mean of each sample in Exercise
Find the probability distribution of the population of six sample mean grand prizes.
If you select two envelopes, what is the probability that you will receive a sample mean grand prize of at least 50 thousand dollars?
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?
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 m, 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
n 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
Write formulas that express the central tendency and variability of the population of all possible sample proportions. Explain what each of these formulas means in your own words.
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 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. In Exercise 7.25 In each of the following cases, find the mean, variance, and standard deviation of the sampling distribution of the sample proportion a. p =.5, n
Suppose that we will randomly select a sample of n 100 elements from a population and that we will compute the sample proportion p ˆ 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 p. Why
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 reports on improvements in customer satisfaction and loyalty made by Bank of America. Akey measure of customer satisfaction is the response (on a scale from 1 to 10) to the question: “ Considering all the business you do with Bank of America, what is your overall satisfaction
In the page margin, we list 15 companies that have historically performed well in the food, drink, and tobacco industries. Consider the random numbers given in the random number table of Table 7.1(a) on page 260. Starting in the upper left corner of Table 7.1(a) and moving down the two leftmost
Again consider the survey of 350 Bank of America customers discussed in Exercise 7.29, 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 7.30, would it be reasonable to state that the survey’s “margin of error” is +-3 percentage points? + - 6 percentage points? Explain.
An article in Fortune magazine discussed “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 best- in- world standards while avoiding huge
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 developing managerial
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.
Explain why it is important to calculate a confidence interval.
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
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
Explain how each of the following changes as the number of degrees of freedom describing a t curve increases: a. The standard deviation of the t curve. b. The points tα and tα/2.
Using Table A. 4 (page 608), find t.100, t .025, and t.001 based on 11 degrees of freedom. Also, find these t points based on 6 degrees of freedom.
Suppose that for a sample of n = 11 measurements, we find that x-bar = 72 and s = 5. Assuming normality, compute confidence intervals for the population mean m 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
Air traffic controllers have the crucial task of ensuring that aircraft don’t collide. To do this, they must quickly discern when two planes are about to enter the same air space at the same time. They are aided by video display panels that track the aircraft in their sector and alert the
Whole Foods is an all- natural grocery chain that has 50,000 square foot stores, up from the industry average of 34,000 square feet. Sales per square foot of supermarkets average just under $ 400 per square foot, as reported by USA Today in an article on “A whole new ballgame in grocery
A production supervisor at a major chemical company wishes to determine whether a new catalyst, catalyst XA-100, increases the mean hourly yield of a chemical process beyond the current mean hourly yield, which is known to be roughly equal to, but no more than, 750 pounds per hour. To test the new
The mean and the standard deviation of the sample of 65 customer satisfaction ratings in Table are 42.95 and 2.6424, respectively. Calculate a t-based 95 percent confidence interval for μ, the mean of all possible customer satisfaction ratings for the XYZ- Box video game system. Are we 95 percent
The mean and the standard deviation of the sample of 100 bank customer waiting times in Table are 5.46 and 2.475, respectively. Calculate a t-based 95 percent confidence interval for μ, the mean of all possible bank customer waiting times using the new system. Are we 95 percent confident that μ
The mean and the standard deviation of the sample of 40 trash bag breaking strengths in Table 1.9 are 50.575 and 1.6438, respectively.a. Use the Excel output in Figure to calculate a t-based 95 percent confidence interval for μ, the mean of the breaking strengths of all possible new trash bags.
Explain what is meant by the margin of error for a confidence interval. What error are we talking about in the context of an interval for μ?
Explain exactly what we mean when we say that a sample of size n makes us 99 percent confident that x̅ is within E units of μ.
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
Referring to Exercise 8.11a, assume that the population standard deviation equals 33. How large a random sample of public owner-controlled companies is needed to make us? In exercise Suppose that a random sample of 100 public owner- controlled companies in New Zealand is found to give a mean audit
Under what conditions is the confidence interval [± zα/2 (σ/√n)] for μ valid?
Referring to Exercise 8.12b (page 299), assume that the population standard deviation equals .66. How large a sample of late replacement buyers is needed to make us? In exercise Suppose that a random sample of 500 late replacement buyers yields a mean number of dealers visited equal to 4.3, and
Referring to Exercise 8.21 (page 307), regard the sample of five trial runs (which has standard deviation 19.65) as a preliminary sample. Determine the number of trial runs of the chemical process needed to make us: In exercise A production supervisor at a major chemical company wishes to
Referring to Exercise 8.20, regard the sample of 10 sales figures (which has standard deviation 32.866) as a preliminary sample. How large a sample of sales figures is needed to make us 95 percent confident that x-bar, the sample mean sales dollars per square foot, is within a margin of error of $
Referring to Exercise 8.19, regard the sample of 15 alert times (which has standard deviation 1.026) as a preliminary sample. Determine the sample size needed to make us 95 percent confident that x-bar, the sample mean alert time, is within a margin of error of .3 second of μ, the population mean
a. What does a population proportion tell us about the population? b. Explain the difference between p and p̂. c. What is meant when a public opinion poll’s margin of error is 3 percent?
Suppose we are using the sample size formula in the box on page 313 to find the sample size needed to make the margin of error in a confidence interval for p equal to E. In each of the following situations, explain what value of p would be used in the formula for finding n: a. We have no idea what
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 311 to compute a confidence interval for p. a. p̂ = .1, n = 30 b. p̂ = .1, n = 100 c. p̂ = .5, n = 50 d. p̂ = .8, n = 400 e. p̂ = .9, n = 30 f.
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 = 100 d. p̂ = .6 and n = 50
In a news story distributed by the Washington Post, Lew Sichelman reports that a substantial fraction of mortgage loans that go into default within the first year of the mortgage were approved on the basis of falsified applications. For instance, loan applicants often exaggerate their income or
Suppose that 60 percent of 1,000 randomly selected U.S. adults say that they take part in some form of daily activity to keep physically fit. Based on this finding, find a 95 percent confidence interval for the proportion of all U.S. adults who would say they take part in some form of daily
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
Consider the marketing ethics case described in Example 8.8. One of the scenarios presented to the 205 marketing researchers is as follows:A marketing testing firm to which X company gives most of its business recently went public. The marketing research director of X company had been looking for a
In an article in CA Magazine, Neil Fitzgerald surveyed Scottish business customers concerning their satisfaction with aspects of their banking relationships. Fitzgerald reports that, in 418 telephone interviews conducted by George Street Research, 67 percent of the respondents gave their banks a
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
Consumer Reports (January 2005) indicates that profit margins on extended warranties are much greater than on the purchase of most products. In this exercise we consider a major electronics retailer that wishes to increase the proportion of customers who buy extended warranties on digital cameras.
Consider Exercise 8.39 and suppose we wish to find the sample size n needed in order to be 95 percent confident that the sample proportion of respondents who said they took part in some sort of daily activity to keep physically fit, is within a margin of error of .02 of p, the proportion of all U.
Referring to Exercise 8.44, determine the sample size needed in order to be 99 percent confident that p̂, 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 proportion of all sets that last at
Suppose we conduct a poll to estimate the proportion of voters who favor a major presidential candidate. Assuming that 50 percent of the electorate could be in favor of the candidate, determine the sample size needed so that we are 95 percent confident that p̂, the sample proportion of voters who
Explain why the finite population correction√(N – n) / N is unnecessary when the sample size is less than 5 percent of the population size. Give an example using numbers.
A retailer that sells audio and video equipment 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
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
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
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
A random sample of 50 perceived age estimates for a model in a cigarette advertisement showed that the sample mean and sample standard deviation were 26.22 years and 3.7432 years, respectively. a. Use this sample to calculate a 95 percent confidence interval for the population mean age estimate for
How safe are child car seats? Consumer Reports (May 2005) tested the safety of child car seats in 30 mph crashes. They found “slim safety margins” for some child car seats. Suppose that Consumer Reports simulates the safety of the market- leading child car seat. Their test consists of placing
Suppose that, for a sample of size n = 100 measurements, we find that x-bar = 50. Assuming that s equals 2, calculate confidence intervals for the population mean m with the following confidence levels:a. 95%b. 99%c. 97%d. 80%e. 99.73%f. 92%
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
Recall that a bank manager has developed a new system to reduce the time customers spend waiting to be served by tellers during peak business hours. The mean waiting time during peak business hours under the current system is roughly 9 to 10 minutes. The bank manager hopes that the new system will
The mean of the sample of 65 customer satisfaction ratings in Table 1.7 is 42.95. If we let m denote the mean of all possible customer satisfaction ratings for the XYZ Box video game system, and assume that the population standard deviation equals 2.64:a. Calculate 95 percent and 99 percent
Define each of the following: Type I error, α, Type II error, β.
Suppose that we wish to test H0: μ = 80 versus Ha: μ > 80, where the population standard deviation is known to equal 20. Also, suppose that a sample of 100 measurements randomly selected from the population has a mean equal to 85.a. Calculate the value of the test statistic z.b. By comparing z
Suppose that we wish to test H0: μ = 20 versus Ha: μ < 20, where the population standard deviation is known to equal 7. Also, suppose that a sample of 49 measurements randomly selected from the population has a mean equal to 18.a. Calculate the value of the test statistic z.b. By comparing z
Suppose that we wish to test H0: μ = 40 versus Ha: μ ≠ 40, where the population standard deviation is known to equal 18. Also, suppose that a sample of 81 measurements randomly selected from the population has a mean equal to 35.a. Calculate the value of the test statistic z.b. By comparing z
Recall that “very satisfied” customers give the XYZ-Box video game system a rating that is at least 42. Suppose that the manufacturer of the XYZ-Box wishes to use the random sample of 65 satisfaction ratings to provide evidence supporting the claim that the mean composite satisfaction rating
Recall that a bank manager has developed a new system to reduce the time customers spend waiting for teller service during peak hours. The manager hopes the new system will reduce waiting times from the current 9 to 10 minutes to less than 6 minutes. Suppose the manager wishes to use the random
Consolidated Power, a large electric power utility, has just built a modern nuclear power plant. This plant discharges waste water that is allowed to flow into the Atlantic Ocean. The Environmental Protection Agency (EPA) has ordered that the waste water may not be excessively warm so that thermal
Do part b of Exercise 9.15 if the sample mean equals 60.262. In par b exercise Suppose that Consolidated Power decides to use a level of significance of a .05, and suppose a random sample of 100 temperature readings is obtained. If the sample mean of the 100 temperature readings is 60.482, test
Do part b of Exercise 9.15 if the sample mean equals 60.618. In par b exercise Suppose that Consolidated Power decides to use a level of significance of a .05, and suppose a random sample of 100 temperature readings is obtained. If the sample mean of the 100 temperature readings is 60.482, test H0
An automobile parts supplier owns a machine that produces a cylindrical engine part. This part is supposed to have an outside diameter of three inches. Parts with diameters that are too small or too large do not meet customer requirements and must be rejected. Lately, the company has experienced
The Crown Bottling Company has just installed a new bottling process that will fill 16- ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and underfilling bottles are undesirable: Underfilling leads to customer complaints and overfilling costs the company considerable
When testing a hypothesis, why don’t we set the probability of a Type I error to be extremely small? Explain.
National Motors has equipped the ZX-900 with a new disk brake system. We define m to be the mean stopping distance (from a speed of 35 mph) of all ZX-900s. National Motors would like to claim that the ZX-900 achieves a shorter mean stopping distance than the 60 ft claimed by a competitor.a. Set up
What assumptions must be met in order to carry out a t test about a population mean?
How do we decide whether to use a z test or a t test when testing a hypothesis about a population mean?
Suppose that a random sample of nine measurements from a normally distributed population gives a sample mean of 2.57 and a sample standard deviation of .3. Use critical values to test H0: μ = 3 versus Ha: μ ≠ 3 using levels of significance α = .10, α = .05, α = .01, and α = .001.
Consider the e- billing case. The mean and the standard deviation of the sample of 65 payment times are 18.1077 and 3.9612, respectively.(1) Test H0: μ < 19.5 versus Ha: μ < 19.5 by setting a equal to .01 and using a critical value rule.(2) Interpret the (computer calculated) p-value of
Consider the trash bag case. The mean and the standard deviation of the sample of 40 trash bag breaking strengths are 50.575 and 1.6438, respectively.(1) Test H0: μ = 50 versus Ha: μ = 50 by setting α equal to .05 and using a critical value rule.(2) Interpret the (computer calculated) p-value of
Recall that it is hoped that the mean alert time, m, using the new display panel is less than eight seconds.(1) Formulate the null hypothesis H0 and the alternative hypothesis Ha that would be used to attempt to provide evidence that m is less than eight seconds.(2) Discuss the meanings of a Type I
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 that a random sample of seven Ohio banks is selected and that the bad debt ratios (written as percentages) for these banks are 7%, 4%, 6%,
Recall that “very satisfied” customers give the XYZ-Box video game system a composite satisfaction rating that is at least 42.a. Letting m represent the mean composite satisfaction rating for the XYZ-Box, set up the null and alternative hypotheses needed if we wish to attempt to provide
Recall that “very satisfied” customers give the XYZ-Box video game system a rating that is at least 42. Suppose that the manufacturer of the XYZ-Box wishes to use the 65 satisfaction ratings to provide evidence supporting the claim that the mean composite satisfaction rating for the XYZ-Box
Recall that a bank manager has developed a new system to reduce the time customers spend waiting for teller service during peak hours. The manager hopes the new system will reduce waiting times from the current 9 to 10 minutes to less than 6 minutes.a. Letting μ represent the mean waiting time
Consider a chemical company that wishes to determine whether a new catalyst, catalyst XA-100, changes the mean hourly yield of its chemical process from the historical process mean of 750 pounds per hour. When five trial runs are made using the new catalyst, the following yields (in pounds per
Recall from Exercise 8.12 that Bayus (1991) studied the mean numbers of auto dealers visited by early and late replacement buyers.(1) Letting μ be the mean number of dealers visited by all late replacement buyers, set up the null and alternative hypotheses needed if we wish to attempt to provide
In 1991 the average interest rate charged by U.S. credit card issuers was 18.8 percent. Since that time, there has been a proliferation of new credit cards affiliated with retail stores, oil companies, alumni associations, professional sports teams, and so on. A financial officer wishes to study
Suppose we test H0: p = .3 versus Ha: ≠ .3 and that a random sample of n = 100 gives a sample proportion p-bar = .20.a. Test H0 versus Ha at the .01 level of significance by using critical values. What do you conclude?b. Find the p-value for this test.c. Use the p-value to test H0 versus Ha by

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