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business statistics
Statistics For Management And Economics 9th Edition Gerald Keller, Kenneth C Louden - Solutions
a. The mean and standard deviation of a sample of 100 is and s 300. Estimate the population mean with 95% confidence.b. Repeat part (a) with s 200.c. Repeat part (a) with s 100.d. Discuss the effect on the confidence interval estimate of decreasing the standard deviation s.
a. The mean and standard deviation of a sample of 100 are.Estimate the population mean with 95% confidence.b. Repeat part (a) with s 4.c. Repeat part (a) with s 10.d. Discuss the effect on the confidence interval estimate of increasing the standard deviation s.
a. The sample mean and standard deviation from a random sample of 10 observations from a normal population were computed as and s 9.Calculate the value of the test statistic (and for Excel users, the p-value) of the test required to determine whether there is enough evidence to infer at the 5%
a. A statistics practitioner is in the process of testing to determine whether there is enough evidence to infer that the population mean is different from 180. She calculated the mean and standard deviation of a sample of 200 observations as and s 22. Calculate the value of the test statistic
a. Calculate the test statistic (and for Excel users, the p-value) when , s 50, and n 100.Use a 5% significance level.x = 145 x = 175 x = 23 x = 63 x = 120 x = 10 and s = 1b. Repeat part (a) with .c. Repeat part (a) with .d. What happens to the t-statistic (and for Excel users, the p-value)
a. A random sample of 25 observations was drawn from a normal population. The sample mean and sample standard deviation are and s 15.Calculate the test statistic (and for Excel users, the p-value) of a test to determine if there is enough evidence at the 10% significance level to infer that the
a. A statistics practitioner wishes to test the following hypotheses:A sample of 50 observations yielded the statistics and s 45. Calculate the test statistic(and for Excel users, the p-value) of a test to determine whether there is enough evidence at the 10% significance level to infer that the
a. To test the following hypotheses, a statistics practitioner randomly sampled 100 observations and found and s 35. Calculate the test statistic (and for Excel users, the p-value) of a test to determine whether there is enough evidence at the 1% significance level to infer that the alternative
a. After sampling 1,000 members of a normal population, you find and s 9,950. Estimate the population mean with 90% confidence.b. Repeat part (a) assuming that you know that the population standard deviation is 9,950.c. Explain why the interval estimates were virtually identical.
a. A statistics practitioner randomly sampled 1,500 observations and found and s 25. Test to determine whether there is enough evidence at the 5% significance level to infer that the population mean is less than 15.b. Repeat part (a) assuming that you know that the population standard deviation
a. Test the following hypotheses with .05 given that , s 100, and n 1,000.b. Repeat part (a) assuming that you know that the population standard deviation is 100.c. Explain why the conclusions produced in parts(a) and (b) are virtually identical.Applications The following exercises may
Xr12-23 A courier service advertises that its average delivery time is less than 6 hours for local deliveries. A random sample of times for 12 deliveries to an address across town was recorded. These data are shown here.Is this sufficient evidence to support the courier’s advertisement, at the 5%
Xr12-24 How much money do winners go home with from the television quiz show Jeopardy? To determine an answer, a random sample of winners was drawn; the recorded amount of money each won is listed here. Estimate with 95% confidence the mean winnings for all the show’s players.26,650 6,060 52,820
Xr12-25 A diet doctor claims that the average North American is more than 20 pounds overweight. To test his claim, a random sample of 20 North Americans was weighed, and the difference between their actual and ideal weights was calculated. The data are listed here. Do these data allow us to infer
Xr12-26 A federal agency responsible for enforcing laws governing weights and measures routinely inspects packages to determine whether the weight of the contents is at least as great as that advertised on the package. A random sample of 18 containers whose packaging states that the contents weigh
Xr12-27 A parking control officer is conducting an analysis of the amount of time left on parking meters. A quick survey of 15 cars that have just left their metered parking spaces produced the following times (in minutes). Estimate with 95% confidence the mean amount of time left for all the
Xr12-28 Part of a university professor’s job is to publish his or her research. This task often entails reading a variety of journal articles to keep up to date. To help determine faculty standards, a dean of a business school surveyed a random sample of 12 professors across the country and asked
Xr12-29 Most owners of digital cameras store their pictures on the camera. Some will eventually download these to a computer or print them using their own printers or a commercial printer. A film-processing company wanted to know how many pictures were stored on computers. A random sample of 10
Xr12-30 University bookstores order books that instructors adopt for their courses. The number of copies ordered matches the projected demand.However, at the end of the semester, the bookstore has too many copies on hand and must return them to the publisher. A bookstore has a policy that the
Xr12-33 A random sample of American adults was asked whether or not they smoked cigarettes. Those who responded affirmatively were asked how many cigarettes they smoked per day. Assuming that there are 50 million American adults who smoke, estimate with 95% confidence the number of cigarettes
Xr12-35* OfficeMax, a chain that sells a wide variety of office equipment often features sales of products whose prices are reduced because of rebates. Some rebates are so large that the effective price becomes $0.The goal is to lure customers into the store to buy other nonsale items. A secondary
Xr12-36 An increasing number of North Americans regularly take vitamins or herbal remedies daily.To gauge this phenomenon, a random sample of Americans was asked to report the number of vitamin and herbal supplements they take daily.Estimate with 95% confidence the mean number of vitamin and herbal
Xr12-37 Generic drug sales make up about half of all prescriptions sold in the United States. The marketing manager for a pharmaceutical company wanted to acquire more information about the sales of generic prescription drugs. To do so, she randomly sampled 900 customers who recently filled
Xr12-38 Traffic congestion seems to worsen each year. This raises the question, How much does roadway congestion cost the United States annually?The Federal Highway Administration’s Highway Performance Monitoring System conducts an analysis to produce an estimate of the total cost. Drivers in the
Xr12-39 To help estimate the size of the disposable razor market, a random sample of men was asked to count the number of shaves they used each razor for.Assume that each razor is used once per day.Estimate with 95% confidence the number of days a pack of 10 razors will last.
Xr12-41 On a per capita basis, the United States spends far more on health care than any other country.To help assess the costs, annual surveys are undertaken. One such survey asks a sample of Americans to report the number of times they visited a health-care professional in the year. The data for
Xr12-42 Companies that sell groceries over the Internet are called e-grocers. Customers enter their orders, pay by credit card, and receive delivery by truck. A potential e-grocer analyzed the market and determined that the average order would have to exceed $85 if the e-grocer were to be
Xr12-44 In 2010, most Canadian cities were experiencing a housing boom. As a consequence, home buyers were required to borrow more on their mortgages.To determine the extent of this problem, a survey of Canadian households was undertaken wherein household heads were asked to report their total
Xr12-45 Refer to Exercise 12.44. In addition to household debt, the survey asked each household to report the debt-to-income ratio. Estimate with 90% confidence the mean debt-to-income ratio.
GSS2008* In 2008, respondents were asked to report the number of years of education (EDUC). Do the data provide enough evidence at the 5% significance level to infer that the average American adult completed more than 12 years of education?
GSS2008* Estimate with 95% confidence the mean numbers of earners (EARNRS) in the household in 2008.
GSS2008* Can we infer at the 5% significance level that the mean number of hours worked (HRS) among those working full- or part-time is greater than 40?
GSS2006* Estimate with 95% confidence the mean number of years in current job (YEARSJOB) in 2006.
GSS2006* Estimate with 90% confidence the mean number of hours American adults spend watching television per day (TVHOURS).
ANES2008* Can we infer with .05 that the average American has completed more than 12 years of education(EDUC)?
ANES2008* Estimate with 95% confidence the mean number of days in a typical week (DAYS8) spent by American adults watching the national news on television, not including sports.
ANES2008* Estimate with 99% confidence the mean amount of time in a typical day spent by American adults watching or reading news on the Internet(TIME1).
2-test of 2. Inputs: sample variance, sample size, and hypothesized variance.Outputs: Test statistic, critical values, and one- and two-tail p-values. Tools: CHIINV, CHITEST.
2-estimate of 2. Inputs: sample variance, sample size, and confidence level. Outputs:Upper and lower confidence limits. Tools:CHIINV.
a. Estimate 2 with 90% confidence given that n 15 and s2 12.b. Repeat part (a) with n 30.c. What is the effect of increasing the sample size?Applications
Xr12-59 The weights of a random sample of cereal boxes that are supposed to weigh 1 pound are listed here. Estimate the variance of the entire population of cereal box weights with 90% confidence.1.05 1.03 .98 1.00 .99 .97 1.01 .96
Xr12-60 After many years of teaching, a statistics professor computed the variance of the marks on her final exam and found it to be 2 250. She recently made changes to the way in which the final exam is marked and wondered whether this would result in a reduction in the variance. A random
Xr12-61 With gasoline prices increasing, drivers are more concerned with their cars’ gasoline consumption.For the past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill-up to fill-up was 2 23 mpg2. Now that his car is 5 years old, he would like to
Xr12-62 During annual checkups, physicians routinely send their patients to medical laboratories to have various tests performed. One such test determines the cholesterol level in patients’ blood. However, not all tests are conducted in the same way. To acquire more information, a man was sent to
Xr12-64 Some traffic experts believe that the major cause of highway collisions is the differing speeds of cars. In other words, when some cars are driven slowly while others are driven at speeds well in excess of the speed limit, cars tend to congregate in bunches, increasing the probability of
Xr12-65 The job placement service at a university observed the not unexpected result of the variance in marks and work experience of the university’s graduates: Some graduates received numerous offers, whereas others received far fewer. To learn more about the problem, a survey of 90 recent
z-test of p. Inputs: sample proportion, sample size, and hypothesized proportion.Outputs: Test statistic, critical values, and one- and two-tail p-values. Tools: NORMINV, NORMSDIST.
z-estimate of p. Inputs: sample proportion, sample size, and confidence level. Outputs:Upper and lower confidence limits. Tools:NORMINV.
a. The proportion of successes in a random sample of 400 was calculated as 50%. Estimate the population proportion with 95% confidence.b. Repeat part a with .c. Repeat part a with .d. Discuss the effect on the width of the confidence interval estimate of reducing the sample proportion.
a. Calculate the p-value of the test of the following hypotheses given that and n 100:b. Repeat part (a) with n 200.H1: p 7 .60 H0: p = .60 pN = .63 pN = 10%pN = 33%c. Repeat part (a) with n 400.d. Describe the effect on the p-value of increasing the sample size.
a. A statistics practitioner wants to test the following hypotheses:A random sample of 100 produced .Calculate the p-value of the test.b. Repeat part (a) with .c. Repeat part (a) with .d. Describe the effect on the z-statistic and its p-value of decreasing the sample proportion.
Suppose that you used the sample size calculated in Exercise 12.74 and found .a. Estimate the population proportion with 90%confidence.b. Is this the result you expected? Explain.
Suppose that you used the sample size calculated in Exercise 12.74 and found .a. Estimate the population proportion with 90%confidence.b. Is this the result you expected? Explain.c. If you were hired to conduct this analysis, would the person who hired you be satisfied with the interval estimate
Redo Exercise 12.74 assuming that you know that the sample proportion will be no less than .75.
Suppose that you used the sample size calculated in Exercise 12.77 and found .a. Estimate the population proportion with 90%confidence.b. Is this the result you expected? Explain.
Suppose that you used the sample size calculated in Exercise 12.77 and found .a. Estimate the population proportion with 90%confidence.b. Is this the result you expected? Explain.c. If you were hired to conduct this analysis, would the person who hired you be satisfied with the interval estimate
Suppose that you used the sample size calculated in Exercise 12.77 and found .a. Estimate the population proportion with 90%confidence.b. Is this the result you expected? Explain.c. If you were hired to conduct this analysis, would the person who hired you be satisfied with the interval estimate
A statistics practitioner working for major league baseball wants to supply radio and television commentators with interesting statistics. He observed several hundred games and counted the number of times a runner on first base attempted to steal second base. He found 373 such events, 259 of them
A dean of a business school wanted to know whether the graduates of her school used a statistical inference technique during their first year of employment after graduation. She surveyed 314 graduates and asked about the use of statistical techniques.After tallying the responses, she found that 204
Has the recent drop in airplane passengers resulted in better on-time performance? Before the recent economic downturn, one airline bragged that 92% of its flights were on time. A random sample of 165 flights completed this year reveals that 153 were on time. Can we conclude at the 5% significance
Refer to Exercise 12.86. Assuming that there are 1 million travelers per year and the fare is $3.00, estimate with 95% confidence the amount of revenue lost each year.The following exercises require the use of the Wilson estimator.
Spam is of concern to anyone with an e-mail address. Several companies offer protection by eliminating spam e-mails as soon as they hit an inbox. To examine one such product, a manager randomly sampled his daily e-mails for 50 days after installing spam software. A total of 374 e-mails were
A management professor was in the process of investigating the relationship between education and managerial level achieved. The source of his data was a survey of 385 CEOs of medium and large companies. He discovered only one CEO who did not have at least one university degree. Estimate(using a
Xr12-91* There is a looming crisis in universities and colleges across North America. In most places, enrollments are increasing; this requires more instructors. However, there are not enough PhDs to fill the vacancies now. Moreover, among current professors, a large proportion are nearing
Refer to Exercise 12.91. If the number of professors between the ages of 55 and 64 is 75,000, estimate the total number of such professors who plan to retire early.
Xr12-93 According to the Internal Revenue Service, in 2009 the top 5% of American income earners earned more than $153,542, and the top 1% earned more than $388,806. The top 1% pay slightly more than 40% of all federal income taxes. To determine whether Americans are aware of these figures,
Xr12-94 The results of an annual claimant satisfaction survey of policyholders who have had a claim with State Farm Insurance Company revealed a 90% satisfaction rate for claim service. To check the accuracy of this claim, a random sample of State Farm claimants was asked to rate their satisfaction
Xr12-96* An important decision faces Christmas holiday celebrators: buy a real or artificial tree? A sample of 1,508 male and female respondents age 18 years and older was interviewed. Respondents were asked whether they preferred a real (1) or artificial(2) tree. If 6 million Canadian households
Xr12-97* Because television audiences of newscasts tend to be older (and because older people suffer from a variety of medical ailments), pharmaceutical companies’advertising often appears on national news in the three networks (ABC, CBS, and NBC). The ads concern prescription drugs such as those
Xr12-98 A professor of business statistics recently adopted a new textbook. At the completion of the course, 100 randomly selected students were asked to assess the book. The responses are as follows.Excellent (1), Good (2), Adequate (3), Poor (4)The results are stored using the codes in
Refer to Exercise 12.98. Do the data allow us to conclude at the 10% significance level that more than 90% of all business students would rate it as at least adequate?
Xm12-00* Refer to the chapter-opening example.Estimate with 95% confidence the number of television households that were tuned to the Extreme Makeover: Home Edition.
Xr12-101 According to the American Contract Bridge League (ACBL), bridge hands that contain two fourcard suits, one three-card suit and one two-card suit(4-4-3-2) occur with 21.55% probability. Suppose that a bridge-playing statistics professor with much too much time on his hands tracked the
Xr12-102 Chlorofluorocarbons (CFCs) are used in air conditioners. However, CFCs damage the ozone layer, which protects us from the sun’s harmful rays.As a result, many jurisdictions have banned the production and use of CFCs. The latest jurisdiction to do so is the province of Ontario, which has
GSS2008* What is the highest degree you completed(DEGREE)?0 Left high school, 1 High school, 2 Junior college, 3 Bachelor’s degree, 4 Graduate degree Estimate with 95% confidence the number of American adults who did not finish high school.
GSS2008* “Last week were you working full-time, parttime, going to school, keeping house, or what”(WRKSTAT)? The responses were 1 Working fulltime, 2 Working part-time, 3 Temporarily not working, 4 Unemployed, laid off, 5 Retired, 6 School, 7 Keeping house, 8 Other.a. Estimate
GSS2008* Are you self-employed or do you work for someone else (WRKSLF)? 1 Self employed, 2 Someone else. Can we infer that more than 10% of Americans are self-employed?
GSS2008* Are you employed by the federal, state, or local government or by a private employer (WRKGOVT)?1 Government, 2 Private. Estimate with 90% confidence the number of Americans who work for the government.Political Questions PARTYID: Generally speaking, do you think of yourself as a
GSS2008* Is there sufficient evidence to infer that in 2008 more Americans saw themselves as Democrats than Republicans?
GSS2006* Do the data allow us to conclude that in 2006 more Americans identified themselves as Democrats than Republicans?
GSS2004* Is there enough statistical evidence to conclude that in 2004 there were more Democrats than Republicans?
GSS2002* Is there sufficient evidence to infer that in 2002 more Americans saw themselves as Democrats rather than as Republicans?POLVIEW: I’m going to show you a seven-point scale on which the political views that people might hold are arranged from extremely liberal to extremely conservative.
GSS2008* Do the data provide enough statistical evidence to conclude that in 2008 more Americans identified themselves as conservatives?
GSS2006* Do the data provide enough statistical evidence to conclude that in 2006 more Americans identified themselves as conservatives?
GSS2004* Do the data provide enough statistical evidence to conclude that in 2004 more Americans identified themselves as conservatives?
GSS2002* Do the data provide enough statistical evidence to conclude that in 2002 more Americans identified themselves as conservatives?
Write a brief report on what you discovered in Exercises 12.103 to 12.114.
ANES2008* PARTY: Do you think of yourself as a Democrat, a Republican, an Independent, or what?1 Democrat, 2 Republican, 3 Independent, 4 Other party, 5 No preference Is there sufficient evidence to infer that in 2008 more Americans saw themselves as Democrats than as Republicans?
ANES2004* Repeat Exercise 12.116 for 2004.Liberal–conservative self-placement (LIBCON:1 Extremely liberal; 2 Liberal; 3 Slightly liberal;4 Moderate, middle of the road; 5 Slightly conservative;6 Conservative; 7 Extremely conservative. For the following questions, responses 1, 2, and
ANES2008* Can we infer that in 2008 more Americans perceived themselves as conservative than as liberal?
ANES2004* Repeat Exercise 12.118 for 2004.
ANES2008* Do you currently have any kind of health insurance (HEALTH)? 1 Yes, 5 No.Estimate with 95% confidence the number of American adults who do not have health insurance.
ANES2008* How often do you vote (OFTEN)? 1 Always, 2 Nearly always, 3 Part of the time, 4 Seldom. Can we infer from the data that fewer than 50% of American adults always vote?
ANES2004* In the 2004 presidential election, George W. Bush received 51% of the vote. The American National Election Survey asked some of those surveyed before the election for whom they voted(WHOVOTED). 1 John Kerry, 3 George W. Bush, 5 Ralph Nader, 7 other. Can we infer that the survey
ANES2008* In the 2008 presidential election, Barack Obama received 53% of the vote. The American National Election Survey asked some of those surveyed before the election for whom they voted(WHOVOTE). 1 Barack Obama, 3 John McCain, 7 other. Can we infer that the survey results differ from the
Xr12-124 A new credit card company is investigating various market segments to determine whether it is profitable to direct its advertising specifically at each one. One market segment is composed of Hispanic people. The latest census indicates that there are 30,085,000 Hispanic adults (18 and
Xr12-125* A California university is investigating expanding its evening programs. It wants to target people between 25 and 55 years old who have completed high school but did not complete college or university.To help determine the extent and type of offerings, the university needs to know the
Xr12-126* The JC Penney department store chain segments the market for women’s apparel by its identification of values. The three segments are 1. Conservative 2. Traditional 3. Contemporary Questionnaires about personal and family values are used to identify which segment a woman falls
Xr12-127 Most life-insurance companies are leery about offering policies to people 64 and older.When they do, the premiums must be high enough to overcome the predicted length of life.The president of one life-insurance company was thinking about offering special discounts to Americans 64 and older
Xr12-128 An advertising company was awarded the contract to design advertising for Rolls Royce automobiles.An executive in the firm decided to pitch the product not only to the affluent in the United States but also to those who think they are in the top 1% of income earners in the country. A
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