An important decision faces Christmas holiday celebrator: buy a real or artificial tree? A sample of 1,508 male and female respondents 18 years of age and over was interviewed. Respondents were asked whether they preferred a real (1) or artificial (2) tree. If there are 6 million Canadian households that buy Christmas trees, estimate with 95% confidence the total number of Canadian households that would prefer artificial Christmas trees.
> A rock promoter is in the process of deciding whether to book a new band for a rock concert. He knows that this band appeals almost exclusively to teenagers. According to the latest census, there are 400,000 teenagers in the area. The promoter decides to
> An oil company sends out monthly statements to its customers who purchased gasoline and other items using the company’s credit card. Until now, the company has not included a preaddressed envelope for returning payments. The average and the standard devi
> An advertisement for a major home appliance manufacturer claims that its repair personnel are the loneliest in the world because its appliances require the smallest number of service calls. To examine this claim, a researcher drew a random sample of 100
> Refer to Exercise 12.155. Suppose the engineers recoded the data so that springs that were the correct length were recorded as 1, springs that were too long were recorded as 2, and springs that were too short were recorded as 3. Can we infer at the 10% s
> Engineers who are in charge of the production of springs used to make car seats are concerned about the variability in the length of the springs. The springs are designed to be 500 mm long. When the springs are too long, they will loosen and fall out. Wh
> Obesity is defined as having a Body Mass Index (BMI = 30 grams/kilogram2) over 30. A statistics practitioner took a random sample of American adults and classified their BMI as either 1. Under 20, 2. 20–30, 3. Over 30. There are 234,564,000 American adul
> The manager of a branch of a major bank wants to improve service. She is thinking about giving $1 to any customer who waits in line for a period of time that is considered excessive. (The bank ultimately decided that more than 8 minutes is excessive.) Ho
> A national health care system was an issue in recent presidential election campaign and is likely to be a subject of debate for many years. The issue arose because of the large number of Americans who have no health insurance. Under the present system, f
> The routes of postal deliverers are carefully planned so that each deliverer works between 7 and 7.5 hours per shift. The planned routes assume an average walking speed of 2 miles per hour and no shortcuts across lawns. In an experiment to examine the am
> Refer to Exercise 12.148. Also recorded was the amount of time to commute to work on an average day. Estimate with 90% confidence the average commute time. Data from Exercise 12.148: There are 138,592,000 workers in the United States. An economist took
> Refer to Exercise 12.148. Estimate with 95% confidence the number of workers who carpooled to work. Data from Exercise 12.148: There are 138,592,000 workers in the United States. An economist took a random sample of 550 workers and recorded how they com
> There are 138,592,000 workers in the United States. An economist took a random sample of 550 workers and recorded how they commuted to work (1 = drive alone, 2 = car pool, 3 = public transportation, 4 = walked, 5 = other, and 6 = worked at home). Is ther
> A random sample of complaints about American airlines was drawn and the type of complaint was recorded (1 = Flight problems (cancellations, delays, etc.), 2 = Customer service (unhelpful employees, inadequate means, or cabin service, treatment of delayed
> In a large state university (with numerous campuses), the marks in an introductory statistics course are normally distributed with a mean of 68%. To determine the effect of requiring students to pass a calculus test (which at present is not a prerequisit
> Opinion Research International surveyed people whose household incomes exceed $50,000 and asked each for their top money-related new year’s resolutions. The responses are: 1. Get out of credit card debt 2. Retire before age 65 3. Die broke 4. Make do wit
> Refer to Exercise 12.143. A sample of 425 pickup trucks and SUVs was drawn and the age of the vehicles was recorded. Estimate with 95% confidence the mean age of trucks and SUVs. Data from Exercise 12.143: An important factor in attempting to predict the
> An important factor in attempting to predict the demand for new cars is the age of the cars already on the road. A random sample of 650 cars was drawn and the age of each car was recorded. Estimate with 99% confidence the age means age of all-American ca
> Refer to Exercise 12.151. Also recorded was the weapon used (1 = firearm, 2 = knife or other cutting instrument, 3 = other, 4 = no weapon). Estimate with 90% confidence the number of crimes where a firearm was not used. Data from Exercise 12.151: The ro
> According to FBI statistics, there were 354,520 robberies in the United States in 2012 (latest statistics available). A random sample of robberies was drawn and the amount of loss was recorded. Estimate with 95% confidence the total loss of all the robbe
> Robots are being used with increasing frequency on production lines to perform monotonous tasks. To determine whether a robot welder should replace human welders in producing automobiles, an experiment was performed. The time for the robot to complete a
> There are 604,474 bridges in the United States. A structural engineering team randomly SAMPLED 850 bridges and categorized each as either structurally deficient (restricted to light vehicles, require immediate rehabilitation to remain open, or are closed
> One of the issues that came up in a recent municipal election was the high cost of housing. A candidate seeking to unseat an incumbent claimed that the average family spends more than 30% of its annual income on housing. A housing expert was asked to inv
> Hazardous materials are constantly being around the country. To help determine how dangerous these events are a statistics practitioner recorded the distances of a random sample of trucks, trains, airplanes, and boats carrying explosives. Estimate with 9
> The National Hockey League’s Florida Panthers play in the BB&T center. The cost of parking is $20. However, Lexus occasionally pays the cost by offering free parking to drivers of Lexus cars. A statistician wanted to estimate the cost of this program. He
> Suppose the survey in the previous exercise also asked those who were not in the top 1% whether they believed that within 5 years they would be in the top 1% (1 = will not be in top 1% within 5 years and 2 = will be in top 1% within 5 years). Estimate wi
> 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 i
> Xis normally distributed with mean 100 and standard deviation 20. What is the probability that X is greater than 145?
> 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 whic
> 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,
> 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 of the market segments is composed of Hispanic people. According to the United States census,
> Find the probability. P(Z > 4.0)
> Find the probability. P(Z > 0)
> Find the probability. P(Z > 3.09)
> P(−0.71 < Z < −0.33)
> Find the probability. P(1.04 < Z < 2.03)
> Find the probability. P(Z < 2.57)
> Find the probability. P(Z > 1.87)
> Find the probability. P(Z < 2.23)
> Find the probability. P(Z > −1.24)
> Find the probabilities. P(−1.30 < Z < .70)
> Find the probability. P(Z < −2.16)
> Find the probabilities. P(Z < −1.80)
> Find the probabilities. P(Z < −1.39)
> 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
> According to the American Contract Bridge League (ACBL) bridge hands that contain two 4-card suits, one 3-card suit and one 2-card suit (4-4-3-2) occur with 21.55% probability. Suppose that a bridge-playing statistics professor with too much time on his
> Find the probability. P(Z < 1.60)
> Refer to Exercise 12.112. Do the data allow us to conclude that more than 90% of all business students would rate it as at least adequate? Data from Exercise 12.112: A professor of business statistics recently adopted a new textbook. At the completion o
> 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
> 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 concer
> An increasing number of people are giving gift certificates as Christmas presents. To measure the extent of this practice, a random sample of people was asked (survey conducted December 26–29) whether they had received a gift certificate for Christmas. T
> 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
> Use a computer to find the following values of F. a. F.05, 70, 70 b. F.01, 45, 100 c. F.025, 36, 50 d. F.05, 500, 500
> According to the Internal Revenue Service (IRS) 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 Amer
> Refer to Exercise 12.105. 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. Data from Exercise 12.105: There is a looming crisis in universities and colleges acros
> There is a looming crisis in universities and colleges across North America. In most places’ enrollments are increasing requiring more instructors. However, there are not enough PhDs to fill the vacancies now. Moreover, among current professors, a large
> Refer to Exercise 12.103. Those who hate or dislike doing their taxes were asked the reason. The responses are: 1 = Pay too much taxes, 2 = Complicated/too much paperwork, 3 = Inconvenient/ time consuming, 4 = Don’t like how government uses tax money, 5
> A national survey conducted by Pew Research asked a random sample of 974 American adults how they felt about doing their taxes. The responses are: 1 = Love it, 2 = Like it, 3 = Neither like nor dislike it, 4 = Dislike it, 5 = Hate it. There are 234,564,0
> 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 that there was only one CEO who did
> 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
> In Chapter 6, we discussed how an understanding of probability allows one to properly interpret the results of medical screening tests. The use of Bayes’s Law requires a set of prior probabilities, which are based on historical records. Suppose that a ph
> Refer to Exercise 12.98. 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. Data from Exercise 12.98: The GO transportation system of buses and commuter trains op
> The GO transportation system of buses and commuter trains operates on the honor system. Train travelers are expected to buy their tickets before boarding the train. Only a small number of people will be checked on the train to see whether they bought a t
> What type of educational background do CEOs have? In one survey, 344 CEOs of medium and large companies were asked whether they had an MBA degree. There were 97 MBAs. Estimate with 95% confidence the proportion of all CEOs of medium and large companies w
> Has the recent drop in airplane passengers resulted in better on-time performance? Before the recent 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
> 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. Af
> In some states, the law requires drivers to turn on their headlights when driving in the rain. A highway patrol officer believes that less than one-quarter of all drivers follow this rule. As a test, he randomly samples 200 cars driving in the rain and c
> 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
> Suppose that you used the sample size calculated in Exercise 12.89 and found p^ = .5. 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
> Suppose that you used the sample size calculated in Exercise 12.89 and found p^ = .92. 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
> Suppose that you used the sample size calculated in Exercise 12.89 and found p^ = .75. a. Estimate the population proportion with 90% confidence. b. Is this the result you expected? Explain.
> Re-do Exercise 12.86 assuming that you know that the sample proportion will be no less than .75. Data from Exercise 12.86: Determine the sample size necessary to estimate a population proportion to within .03 with 90% confidence assuming you have no kno
> Suppose that you used the sample size calculated in Exercise 12.86 and found p^ = .75. 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
> Suppose that you used the sample size calculated in Exercise 12.86 and found p^ = .5. a. Estimate the population proportion with 90% confidence. b. Is this the result you expected? Explain.
> Determine the sample size necessary to estimate a population proportion to within .03 with 90% confidence assuming you have no knowledge of the approximate value of the sample proportion.
> a. A statistics practitioner wants to test the following hypotheses: H0: p = .70 H1: p > .70 A random sample of 100 produced p^ = .73. Calculate the p-value of the test. b. Repeat part (a) with p^ = .72. c. Repeat part (a) with p^ = .71. d. Describe the
> a. Calculate the p-value of the test of the following hypotheses given that p^ = .63 and n = 100: H0: p = .60 H1: p > .60 b. Repeat part (a) with n = 200. c. Repeat part (a) with n = 400. d. Describe the effect on the p-value of increasing the sample siz
> 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 p^ = 33%. c. Repeat part (a) with p^ = 10%. d. Discuss the effect on the width of the confiden
> a. In a random sample of 200 observations, we found the proportion of successes to be 48%. Estimate with 95% confidence the population proportion of successes. b. Repeat part (a) with n = 500. c. Repeat part (a) with n = 1000. d. Describe the effect on t
> Home blood-pressure monitors have been on the market for several years. This device allows people with high blood pressure to measure their own and determine whether additional medication is necessary. Concern has been expressed about inaccurate readings
> One problem facing the manager of maintenance departments is when to change the bulbs in streetlamps. If bulbs are changed only when they burn out, it is quite costly to send crews out to change only one bulb at a time. This method also requires someone
> 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 pr
> Some traffic experts believe that the major cause of highway collisions is the differing speeds of cars. That is, 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, in
> One important factor in inventory control is the variance of the daily demand for the product. A management scientist has developed the optimal order quantity and reorder point, assuming that the variance is equal to 250. Recently, the company has experi
> 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 m
> 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
> 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 redu
> 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
> 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?
> a. The sample variance of a random sample of 50 observations from a normal population was found to be s2 = 80. Can we infer at the 1% significance level that _2 is less than 100? b. Repeat part (a) increasing the sample size to 100. c. What is the effect
> a. A random sample of 100 observations was drawn from a normal population. The sample variance was calculated to be s2 = 220. Test with _ = .05 to determine whether we can infer that the population variance differs from 300. b. Repeat Part a changing the
> The manager of a restaurant believes that waiters and waitresses who introduce themselves by telling customers their names will get larger tips than those who don’t. In fact, she claims that the average tip for the former group is 18%, whereas that of th
> a. Determine β for the following test of hypothesis, given that μ = 310: H0: μ = 300 H1: μ > 300 The statistics practitioner knows that the population standard deviation is 50, the significance level is 5%, and the sample size is 81. b. Repeat part (a) w
> a. Find the probability of a Type II error for the following test of hypothesis, given that μ = 196: H0: μ = 200 H1: μ < 200 The significance level is 10%, the population standard deviation is 30, and the sample size is 25. b. Repeat part (a) with n = 10
> Repeat Exercise 9.64 assuming that the means are 140 and 138, respectively. Data from Exercise 9.64: Suppose that we have two normal populations with the means and standard deviations listed here. If random samples of size 25 are drawn from each populat
> a. Calculate the probability of a Type II error for the following hypotheses when μ = 37: H0: μ = 40 H1: μ < 40 The significance level is 5%, the population standard deviation is 5, and the sample size is 25. b. Repeat part (a) with α = 15%. c. Describe
> A statistics practitioner wants to test the following hypotheses with σ = 20 and n = 100: H0: μ = 100 H1: μ > 100 a. Using α = .10 find the probability of a Type II error when μ = 102. b. Repeat part (a) with α = .02. c. Describe the effect on β of decre
> Repeat Exercise 9.61 with samples of size 100. Data from Exercise 9.61: Independent random samples of 10 observations each are drawn from normal populations. The parameters of these populations are Population 1: μ = 280, σ = 25 Population 2: μ = 270, σ
> Determine β for the following test of hypothesis, given that μ = 48. H0: μ = 50 H1: μ < 50 α = .05, σ = 10, n = 40
> Find the probability of a Type II error for the following test of hypothesis, given that μ = 1,050. H0: μ = 1,000 H1: μ > 1,000 α = .01, σ = 50, n = 25
> Calculate the probability of a Type II error for the following test of hypothesis, given that μ = 203. H0: μ = 200 H1: μ ≠ 200 α = .05, σ = 10, n = 100
