A school-board administrator believes that the average number of days absent per year among students is less than 10 days. From past experience, he knows that the population standard deviation is 3 days. In testing to determine whether his belief is true, he could use one of the following plans: i. n = 100, α = .01 ii. n = 75, α = .05 iii. n = 50, α = .10 Which plan has the lowest probability of a Type II error, given that the true population average is 9 days?
> The 2010 Census showed that the percentage of American adults who had an advanced degree (Read: graduate) was 10.5%. Is there sufficient evidence to infer that by 2013 that figure had been increased (EDUC: 17 = Graduate school)?
> The 2010 census showed that the percentage of Black Americans who did not finish high school was 15.8%. Did this figure decrease by 2013? Conduct a test to determine whether there is enough evidence to infer that the proportion of Black Americans who did
> The proportion of women who did not finish high school was 12.4% according to the census in 2010. Is there enough statistical evidence to conclude that the proportion has decreased in 2013 (HHSEX: 2 = Female; EDCL: 1 = No high school diploma)?
> The birth rate in many countries is falling. This will create problems in the future because there will be less people contributing taxes and more retired people receiving government pensions. The birth rate needed to maintain current population levels i
> Is there a contradiction between the results in Exercises 12.175 and 12.176? Explain.
> Among Liberals and Conservatives only is there enough evidence to infer that there are more Conservatives than Liberals (POLVIEWS3: 1 = Liberal, 3 = Conservative)?
> a. A statistics practitioner calculated the mean and standard deviation from a sample of 51. They are x = 120 and s = 15. Estimate the population mean with 95% confidence. b. Repeat part (a) with a 90% confidence level. c. Repeat part (a) with an 80% con
> Among Democratic and Republicans only is there enough evidence to infer that there are more Democrats than Republicans (PARTYID3: 1 = Democrat, 3 = Republican)? (Caution: Tricky question)
> Is the entrepreneurial spirit of the United States alive and well? Estimate with 95% confidence the number of Americans who work for themselves (WRKSLF: 1 = Self-employed).
> How many people work for the federal, state, or local government? Estimate with 95% confidence the number of adults (18 and over) who work for the federal, state, or local government (WRKGOVT: 1 = Government).
> It has been said that America is a nation of immigrants. Estimate with 95% confidence the number of Americans 18 and over who were born outside the United States (BORN: 2 = Born outside the United States).
> According to the 2010 census, among people who were never married the percentage who did not finish high school was 14.0%. Has the proportion in 2014 increased? Perform a statistical test to answer the question (MARITAL: 5 = Never married; DEGREE: 0 = Le
> An increasing number of women are attending university. Women now outnumber men in most college programs. In the 2010 census, the proportion of women with graduate degrees was 10.2% (The census used “advanced” to represent graduate degrees.) Can we infer
> In the 2010 census, the proportion of divorced White Americans was 10.4%. Has that percentage in 2014 increased? Conduct a statistical test to answer the question (RACE: 1 = White; MARITAL: 3 = Divorced).
> Since 2010 the number of jobs available for people who have not completed high school has decreased. Has this resulted in a change in the proportion of Americans who did not complete high school? Perform a statistical test to answer the question (DEGREE:
> In 2010, the United States was just recovering from the housing debacle. The percentage of home ownership was 65.8%. Is there enough evidence to infer that the proportion of home ownership has changed since then (DWELOWN: 1 = Own)?
> Has the proportion of Americans who were never married changed since the census? Conduct a test to answer the question (MARITAL: 5 = Never married).
> a. The mean and standard deviation of a sample of 100 are x = 10 and s = 1. 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 incr
> V C12-03 virtually all countries have universal government run health-care systems. The United States is one notable exception. This is an issue in every election, with some politicians pushing for the United States to adopt a program similar to Canada&a
> While the executives of Pepsi Cola are trying to decide what to do, the university informs them that a similar offer has gone out to the Coca-Cola Company. Furthermore, if both companies want exclusive rights, a bidding war will take place. The executive
> In the last few years, colleges and universities have signed exclusivity agreements with a variety of private companies. These agreements bind the university to sell that company’s products exclusively on the campus. Many of the agreements involve food a
> The game of roulette consists of a wheel with 38 colored and numbered slots. The numbers are 1 to 36, 0 and 00. Half of the slots numbered 1 to 36 are red and the other half are black. The two “zeros” are green. The wh
> As the U.S. population ages, the number of people needing medical care increases. Unless a cure is found in the next decade, one of the most expensive diseases requiring such care is Alzheimer’s, a form of dementia. To estimate the tota
> Use the χ2 table (Table 5) to find the following values of χ2. a. χ2 .10, 5 b. χ2 .01, 100 c. χ2 .95, 18 d. χ2 .99, 60 Data from Table 5: TABLE 8.5 Critical Values of x35, a and x3
> Use a computer to find the following probabilities. a. P(t141 > .94) b. P(t421 > 2.00) c. P(t1000 > 1.96) d. P(t82 > 1.96)
> Use a computer to find the following probabilities. a. P(t64 > 2.12) b. P(t27 > 1.90) c. P(t159 > 1.33) d. P(t550 > 1.85)
> Use a computer to find the following values of t. a. t.05, 143 b. t.01, 12 c. t.025,∞ d. t.05, 100
> Use a computer to find the following values of t. a. t.10, 15 b. t.10, 23 c. t.025, 83 d. t.05, 195
> a. A statistics practitioner drew a random sample of 400 observations and found that x = 700 and s = 100. Estimate the population mean with 90% confidence. b. Repeat part (a) with a 95% confidence level. c. Repeat part (a) with a 99% confidence level. d.
> Use the t table (Table 4) to find the following values of t. a. t.005, 33 b. t.10, 600 c. t.05, 4 d. t.01, 20
> Use the t table (Table 4) to find the following values of t. a. t.10, 15 b. t.10, 23 c. t.025, 83 d. t.05, 195
> A Jiffy Lube franchise manager is concerned about the amount of time it takes for his technicians to change the oil and filters of cars. The current mean time for the complete operation is 18 minutes. He hasn’t kept track of the number of times his emplo
> Refer to Exercise 8.85. In order to improve the time spent by trucks waiting, both countries should improve the service rate by customs agents. Suppose that the governments decided that the probability that a truck spends more than 30 minutes being check
> The manager of a supermarket tracked the amount of time needed for customers to be served by the cashier. After checking with his statistics professor, he concluded that the checkout times are exponentially distributed with a mean of 6 minutes. What prop
> Calculate the value of the test statistic, set up the rejection region, determine the p-value, interpret the result, and draw the sampling distribution. H0: μ = 15 H1: μ < 15 σ = 2, n = 25, x = 14.3, α = .10
> Because automatic banking machine (ABM) customers can perform a number of transactions, the times to complete them can be quite variable. A banking consultant has noted that the times are exponentially distributed with a mean of 125 seconds. What proport
> The manager of a gas station has observed that the times required by drivers to fill their car’s tank and pay are quite variable. In fact, the times are exponentially distributed with a mean of 7.5 minutes. What is the probability that a car can complete
> Toll booths on the New York State Thruway are often congested because of the large number of cars waiting to pay. A consultant working for the state concluded that if service times are measured from the time a car stops in line until it leaves, service t
> A bank wishing to increase its customer base advertises that it has the fastest service and that virtually all of its customers are served in less than 10 minutes. A management scientist has studied the service times and concluded that service times are
> a. The mean and standard deviation of a sample of 100 is x = 1500 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 o
> Canada and the United States are each other’s largest trading partner. The two-way trade between these two countries is the largest in the world. This makes the Ambassador bridge linking Windsor Ontario and Detroit Michigan extremely busy. The Free Trade
> The time between breakdowns of aging machines is known to be exponentially distributed with a mean of 25 hours. The machine has just been repaired. Determine the probability that the next breakdown occurs more than 50 hours from now.
> The production of a complex chemical needed for anticancer drugs is exponentially distributed with λ = 6 kilograms per hour. What is the probability that the production process requires more than 15 minutes to produce the next kilogram of drugs?
> X is an exponential random variable with λ = .3. Find the following probabilities. a. P(X > 2) b. P(X < 4) c. P(1 < X < 2) d. P(X = 3)
> Let X be an exponential random variable with λ = .5. Find the following probabilities. a. P(X > 1) b. P(X > .4) c. P(X < .5) d. P(X < 2)
> X is an exponential random variable with λ = .25. Sketch the graph of the distribution of X by plotting and connecting the points representing f(x) for x = 0, 2, 4, 6, 8, 10, 15, 20.
> Calculate the value of the test statistic, set up the rejection region, determine the p-value, interpret the result, and draw the sampling distribution. H0: μ = 50 H1: μ > 50 σ = 5, n = 9, x = 51, α = .03
> The number of potential sites for the first-stage test in Exercise 11.78 is quite large and the readings can be expensive. Accordingly, the test is conducted with a sample of 25 observations. Because the second stage cost is high, the significance level
> The feasibility of constructing a profitable electricity producing windmill depends on the mean velocity of the wind. For a certain type of windmill, the mean would have to exceed 20 miles per hour to warrant its construction. The determination of a site
> a. A random sample of 25 was drawn from a population. The sample mean and standard deviation are x = 510 and s = 125. Estimate with 95% confidence. b. Repeat part (a) with n = 50. c. Repeat part (a) with n = 100. d. Describe what happens to the confide
> Refer to Exercise 11.54. A financial analyst has determined that a 2-minute reduction in the average break would increase productivity. As a result, the company would hate to lose this opportunity. Calculate the probability of erroneously concluding that
> The fast-food franchiser in Exercise 11.51 was unable to provide enough evidence that the site is acceptable. She is concerned that she may be missing an opportunity to locate the restaurant in a profitable location. She feels that if the actual mean is
> The test of hypothesis in the SSA example concluded that there was not enough evidence to infer that the plan would be profitable. The company would hate to not institute the plan if the actual reduction was as little as 3 days (i.e., μ = 21). Calculate
> In Exercise 11.47, we tested to determine whether the installation of safety equipment was effective in reducing person-hours lost to industrial accidents. The null and alternative hypotheses were H0: μ = 0 H1: μ < 0 with σ = 6, α = .10, n = 50, and μ =
> Suppose that in Example 11.1 we wanted to determine whether there was sufficient evidence to conclude that the new system would not be costeffective. Set up the null and alternative hypotheses and discuss the consequences of Type I and Type II errors. Co
> Draw the operating characteristic curve for n = 10, 50, and 100 for the following test: H0: μ = 400 H1: μ > 400 α = .05, σ = 50
> For the test of hypothesis H0: μ = 1,000 H1: μ ≠ 1,000 α = .05, σ = 200 draw the operating characteristic curve for n = 25, 100, and 200.
> calculate the value of the test statistic, set up the rejection region, determine the p-value, interpret the result, and draw the sampling distribution. H0: μ = 1000 H1: μ ≠ 1000 σ = 200, n = 100, x = 980, α = .01
> Several years ago, in a high-profile case, a defendant was acquitted in a double-murder trial but was subsequently found responsible for the deaths in a civil trial. (Guess the name of the defendant—the answer is in Appendix C.) In a civil trial the plai
> Many Americans contributed to their 401k investment accounts. An economist wanted to determine how well these investments performed. A random sample of Americans with 401k investments were surveyed and asked to report the total amount invested. Can we in
> You are contemplating a Ph.D. in business or economics. If you succeed, a life of fame, fortune, and happiness awaits you. If you fail, you’ve wasted 5 years of your life. Should you go for it?
> A survey of American consumers asked respondents to report the amount of money they spend on bakery products in a typical month. If we assume that the population standard deviation is $5, can we conclude at the 10% significance level that the mean monthl
> An economist surveyed homeowners in a large city to determine the percentage increase in their heating bills over the last 5 years. The economist particularly wanted to know if there was enough evidence to infer that heating cost increases were greater t
> The current no-smoking regulations in office buildings require workers who smoke to take breaks and leave the building in order to satisfy their habits. A study indicates that such workers average 32 minutes per day taking smoking breaks. The standard de
> The golf professional at a private course claims that members who have taken lessons from him lowered their handicap by more than five strokes. The club manager decides to test the claim by randomly sampling 25 members who have had lessons and asking eac
> Many Alpine ski centers base their projections of revenues and profits on the assumption that the average Alpine skier skis four times per year. To investigate the validity of this assumption, a random sample of 63 skiers is drawn and each is asked to re
> A fast-food franchiser is considering building a restaurant at a certain location. Based on financial analyses, a site is acceptable only if the number of pedestrians passing the location averages more than 100 per hour. The number of pedestrians observe
> For the past few years, the number of customers of a drive-up bank in New York has averaged 20 per hour, with a standard deviation of 3 per hour. This year, another bank 1 mile away opened a drive-up window. The manager of the first bank believes that th
> You are the pilot of a jumbo jet. You smell smoke in the cockpit. The nearest airport is less than 5 minutes away. Should you land the plane immediately?
> An automotive expert claims that the large number of self-serve gasoline stations has resulted in poor automobile maintenance, and that the average tire pressure is more than 4 pounds per square inch (psi) below its manufacturer’s specification. As a qui
> A highway patrol officer believes that the average speed of cars traveling over a certain stretch of highway exceeds the posted limit of 55 mph. The speeds of a random sample of 200 cars were recorded. Do these data provide sufficient evidence at the 1%
> It is the responsibility of the federal government to judge the safety and effectiveness of new drugs. There are two possible decisions: approve the drug or disapprove the drug.
> In an attempt to reduce the number of person-hours lost as a result of industrial accidents, a large production plant installed new safety equipment. In a test of the effectiveness of the equipment, a random sample of 50 departments was chosen. The numbe
> Past experience indicates that the monthly long-distance telephone bill is normally distributed with a mean of $17.85 and a standard deviation of $3.87. After an advertising campaign aimed at increasing long-distance telephone usage, a random sample of 2
> A dean of a business school claims that the Graduate Management Admission Test (GMAT) scores of applicants to the school’s MBA program have increased during the past 5 years. Five years ago, the mean and standard deviation of GMAT scores of MBA applicant
> In the midst of labor–management negotiations, the president of a company argues that the company’s blue-collar workers, who are paid an average of $30,000 per year, are well paid because the mean annual income of all blue-collar workers in the country i
> A manufacturer of lightbulbs advertises that, on average, its long-life bulb will last more than 5,000 hours. To test the claim, a statistician took a random sample of 100 bulbs and measured the amount of time until each bulb burned out. If we assume tha
> Spam e-mail has become a serious and costly nuisance. An office manager believes that the average amount of time spent by office workers reading and deleting spam exceeds 25 minutes per day. To test this belief, he takes a random sample of 18 workers and
> A machine that produces ball bearings is set so that the average diameter is .50 inch. A sample of 10 ball bearings was measured, with the results shown here. Assuming that the standard deviation is .05 inch, can we conclude at the 5% significance level
> The owner of a public golf course is concerned about slow play, which clogs the course and results in selling fewer rounds. She believes the problem lies in the amount of time taken to sink putts on the green. To investigate the problem, she randomly sam
> You are faced with two investments. One is very risky, but the potential returns are high. The other is safe, but the potential is quite limited. Pick one.
> A random sample of 12 second-year university students enrolled in a business statistics course was drawn. At the course’s completion, each student was asked how many hours he or she spent doing homework in statistics. The data are listed here. It is know
> The club professional at a difficult public course boasts that his course is so tough that the average golfer loses a dozen or more golf balls during a round of golf. A dubious golfer sets out to show that the pro is fibbing. He asks a random sample of 1
> A random sample of 18 young adult men (20–30 years old) was sampled. Each person was asked how many minutes of sports he watched on television daily. The responses are listed here. It is known that σ = 10. Test to determine a
> A business student claims that, on average, an MBA student is required to prepare more than five cases per week. To examine the claim, a statistics professor asks a random sample of 10 MBA students to report the number of cases they prepare weekly. The r
> Refer to Example 11.2. Create a table that shows the effect on the test statistic and the p-value of changing the value of the sample mean. Use x = 15.0, 15.5, 16.0, 16.5, 17.0, 17.5, 18.0, 18.5, and 19.0. Data from Example 11.2: FIGURE 11.8 Samplin
> Redo Example 11.2 with a. σ = 2 b. σ = 10 c. What happens to the test statistic and the p-value when σ increases?
> Redo Example 11.2 with a. n = 50 b. n = 400 c. Briefly describe the effect on the test statistic and the p-value when n increases. Data from Example 11.2: FIGURE 11.8 Sampling Distribution for Example 11.2 pvalue -.1170 -1.96 1.19 1.96 Rejection reg
> For the SSA example, create a table that shows the effect on the test statistic and the p-value of decreasing the value of the sample mean. Use x = 22.0, 21.8, 21.6, 21.4, 21.2, 21.0, 20.8, 20.6, and 20.4.
> Redo the SSA example with a. σ = 3 b. σ = 12 c. Discuss the effect on the test statistic and the p-value when σ increases.
> Redo the SSA example with a. σ = 3 b. σ = 12 c. Discuss the effect on the test statistic and the p-value when σ increases.
> You are the centerfielder of the New York Yankees. It is the bottom of the ninth inning of the seventh game of the World Series. The Yanks lead by 2 with 2 outs and men on second and third. The batter is known to hit for high average and runs very well b
> While conducting a test to determine whether a population mean is less than 900, you find that the sample mean is 1,050. a. Can you make a decision on this information alone? Explain. b. If you did calculate the p-value, would it be smaller or larger tha
> Redo Example 11.1 with a. σ = 35 b. σ = 100 c. Describe the effect on the test statistic and the p-value when σ increases. Data from Example 11.1: FIGURE 11.1 Sampling Distribution for Example 11.1 A-170 Rejection re
> Redo Example 11.1 with a. n = 200 b. n = 100 c. Describe the effect on the test statistic and the p-value when n increases. Data from Example 11.1: FIGURE 11.1 Sampling Distribution for Example 11.1 A-170 Rejection region
> a. Calculate the p-value of the test described here. H0: μ = 60 H1: μ > 60 x = 72, n = 25, σ = 20 b. Repeat part (a) with x = 68. c. Repeat part (a) with x = 64. d. Describe the effect on the test statistic and the p-value of the test when the value of x
> a. Find the p-value of the following test given that x = 990, n = 100, and σ = 25. H0: μ = 1000 H1: μ < 1000 b. Repeat part (a) with σ = 50. c. Repeat part (a) with σ = 100. d. Describe what happens to the value of the test statistic and its p-value when
> a. Test these hypotheses by calculating the p-value given that x = 99, n = 100, and σ = 8. H0: μ = 100 H1: μ ≠ 100 b. Repeat part (a) with n = 50. c. Repeat part (a) with n = 20. d. What is the effect on the value of the test statistic and the p-value of
> a. Given the following hypotheses, determine the p-value when x = 21, n = 25, and σ = 5. H0: μ = 20 H1: μ ≠ 20 b. Repeat part (a) with x = 22. c. Repeat part (a) with x = 23. d. Describe what happens to the value of the test statistic and its p-value whe
> a. A statistics practitioner formulated the following hypotheses H0: μ = 200 H1: μ < 200 and learned that x = 190, n = 9, and σ = 50 Compute the p-value of the test. b. Repeat part (a) with σ = 30. c. Repeat part (a) with σ = 10. d. Discuss what happens
