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mathematics
statistics

Statistics For Management And Economics Abbreviated 10th Edition Gerald Keller - Solutions

The number of potential sites for the first-stage test in Exercise 11.66 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 is set at 1%.A financial analysis of the
a. Compute the p-value in order to test the following hypotheses given that x̄ = 52, n = 9, and σ = 5.H0: µ = 50H1: µ > 50b. Repeat part (a) with n = 25.c. Repeat part (a) with n = 100.d. Describe what happens to the value of the test statistic and its p-value when the sample size increases.
a. A statistics practitioner formulated the following hypotheses.H0: µ = 200H1: µ < 200And learned that x̄ = 190, n = 9, and σ = 50Compute the p-value of the test.b. Repeat part (a) with σ = 30.c. Repeat part (a) with σ = 10d. Discuss what happens to the value of the test statistic and its
a. Given the following hypotheses, determine the p-value when x̄ = 21, n = 25, and σ = 5.H0: μ = 20H1: μ ≠ 20b. Repeat part (a) with x̄ = 22.c. Repeat part (a) with x̄ = 23.d. Describe what happens to the value of the test statistic and its p-value when the value of x̄ increases.
a. Test these hypotheses by calculating the p-value given that x̄ = 99, n = 100, and σ = 8H0: μ = 100H1: μ ≠ 100b. 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 the test when the sample size decreases?
a. Find the p-value of the following test given that x̄ = 990, n = 100, and σ = 25.H0: μ = 1000H1: μ < 1000b. 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 the standard deviation increases.
a. Calculate the p-value of the test described here.H0: μ = 60H1: μ > 60x̄ = 72, n = 25, σ = 20b. Repeat part (a) with x̄ = 68.c. Repeat part (a) with x̄ = 64.d. Describe the effect on the test statistic and the p-value of the test when the value of x̄ decreases.
Redo Example 11.1 witha. N = 200b. N = 100c. Describe the effect on the test statistic and the p-value when n increases.
Redo Example 11.1 witha. σ = 35b. σ = 100c. Describe the effect on the test statistic and the p-value when σ increases.
Redo the SSA example witha. n = 100b. n = 500c. What is the effect on the test statistic and the p-value when n increases?
Redo the SSA example witha. σ = 3b. σ = 12c. Discuss the effect on the test statistic and the p-value when σ increases.
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 x̄ = 22.0, 21.8, 21.6, 21.4, 21.2, 21.0, 20.8, 20.6, and 20.4.
Redo Example 11.2 witha. n = 50b. n = 400c. Briefly describe the effect on the test statistic and the p-value when n increases.
Redo Example 11.2 witha. σ = 2b. σ = 10c. What happens to the test statistic and the p-value when σ increases?
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 x̄ = 15.0, 15.5, 16.0, 16.5, 17.0, 17.5, 18.0, 18.5, and 19.0
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 results are exhibited here. Can the professor
A random sample of 18 young adult men (20â€“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 Ïƒ = 10. Test to determine at the 5% significance level whether there is enough statistical
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 15 golfers who just completed their rounds to
A random sample of 12 second-Year University students enrolled in a business statistics course was drawn. At the courseâ€™s completion, each student was asked how many hours he or she spent doing homework in statistics. The data are listed here. It is known that the population standard
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 samples 10 foursomes and measures the amount of
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 that the mean diameter is not .50inch?
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 18Â workers and measures the amount of time each
A manufacturer of light bulbs 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 that the lifetime of this type of bulb has a
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 is less than $30,000. That figure is
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 applicants were 560 and 50, respectively. Twenty
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 25 household bills was taken.a. Do the data
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 number of person-hours lost in the month before and
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% significance level to support the officer’s
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 quick test, 50 tires are examined, and the
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 this will result in a decrease in the number of
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 observed for each of 40 hours was recorded. Assuming
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 report the number of times he or she skied the
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 each to report the reduction in handicap, where
In Exercise 11.39, 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 wereH0: μ = 0H1: μ < 0With σ = 6, α = .10, n = 50, and μ = the mean percentage change. The
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 the relevant probability and describe how the
The fast-food franchiser in Exercise 11.43 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 104, the restaurant is likely to be very
Refer to Exercise 11.46. 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 renovation would not be successful when
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.
a. A random sample of 25 was drawn from a population. The sample mean and standard deviation are x̄ = 510 and s = 125. Estimate µ with 95% confidence.b. Repeat part (a) with n = 50.c. Repeat part (a) with n = 100.d. Describe what happens to the confidence interval estimate when the sample size
a. The mean and standard deviation of a sample of 100 is x̄ = 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 of decreasing the standard deviation s.
a. A statistics practitioner drew a random sample of 400 observations and found that x̄ = 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. What is the effect on the confidence interval
a. The mean and standard deviation of a sample of 100 are x̄ = 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 increasing the standard deviation s.
a. A statistics practitioner calculated the mean and standard deviation from a sample of 51. They are x̄ = 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% confidence level.d. What is the effect on the
a. The sample mean and standard deviation from a sample of 81 observations are x̄ = 63 and s = 8. Estimate e with 95% confidence.b. Repeat part (a) with n = 64.c. Repeat part (a) with n = 36.d. Describe what happens to the confidence interval Estimate when the sample size decreases.
a. The sample mean and standard deviation from a random sample of 10 observations from a normal population were computed as x̄ = 23 and s = 9. Calculate the value of the test statistic of the test required to determine whether there is enough evidence to infer at the 5% significance level that the
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 x̄ = 175 and s = 22. Calculate the value of the test
a. Calculate the test statistic when x̄ = 145, s = 50, and n = 100. Use a 5% significance level.H0: µ = 150H1: µ < 150b. Repeat part (a) with x̄ = 140.c. Repeat part (a) with x̄ = 135.d. What happens to the t-statistic when the sample mean decreases?
a. A random sample of 25 observations was drawn from a normal population. The sample mean and sample standard deviation are x̄ = 52 and s = 15. Calculate the test statistic of a test to determine if there is enough evidence at the 10% significance level to infer that the population mean is not
a. A statistics practitioner wishes to test the following hypotheses:H0: µ = 600H1: µ < 600A sample of 50 observations yielded the statistics x̄ = 85 and s = 45. Calculate the test statistic of a test to determine whether there is enough evidence at the 10% significance level to infer that
a. To test the following hypotheses, a statistics practitioner randomly sampled 100 observations and found x̄ = 106 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
A random sample of 8 observations was drawn from a normal population. The sample mean and sample standard deviation are x̄ = 40 and s = 10.a. Estimate the population mean with 95% confidence.b. Repeat part (a) assuming that you know that the population standard deviation is σ = 10.c. Explain why
a. Estimate the population mean with 90% confidence given the following: x̄ = 175, s = 30 and n = 5.b. Repeat part (a) assuming that you know that the population standard deviation is σ = 30.c. Explain why the interval Estimate produced in part (b) is narrower than that in part (a).
a. After sampling 1,000 members of a normal population, you find x̄ = 15,500 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 σ = 9,950.c. Explain why the interval Estimates were virtually identical.
a. In a random sample of 500 observations drawn from a normal population, the sample mean and sample standard deviation were calculated as x̄ = 350 and s = 100. Estimate the population mean with 99% confidence.b. Repeat part (a) assuming that you know that the population standard deviation is σ =
a. A random sample of 11 observations was taken from a normal population. The sample mean and standard deviation are x̄ = 74.5 and s = 9. Can we infer at the 5% significance level that the population mean is greater than 70?b. Repeat part (a) assuming that you know that the population standard
a. A statistics practitioner randomly sampled 10 observations and found x̄ = 103 and s = 17. Is there sufficient evidence at the 10% significance level to conclude that the population mean is less than 110?b. Repeat part (a) assuming that you know that the population standard deviation is σ =
a. A statistics practitioner randomly sampled 1,500 observations and found x̄ = 14 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
a. Test the following hypotheses with α = .05 given that x̄ = 405, s = 100, and n = 1,000.H0: µ = 400H1: µ > 400b. Repeat part (a) assuming that you know that the population standard deviation is σ = 100.c. Explain why the conclusions produced in parts (a) and (b) are virtually
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 courierâ€™s advertisement, at the 5%
A diet doctor claims that the average North American is core 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 at the 5%
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 8 ounces
University bookstores order books that instructors adopt for their courses. The number of copies ordered catches 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 proportion
A company that produces universal remote controls wanted to determine the number of remote control devices American homes contain. The company hired a statistician to survey 240 randomly selected homes and determine the number of remote controls. If there are 100 million house-holds, Estimate with
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 smoked per
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 non-sale items. A secondary
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
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 99
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.
Because of the enormity of the viewing audience, firms that advertise during the Super Bowl create special commercials that tend to be quite entertaining. Thirty-second commercials cost several million dollars during the Super Bowl game. A random sample of people who watched the game was asked how
On a per capita basis, the United States spends far core on health 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 2009 (latest
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 profitable. To
In 2010, cost Canadian cities were experiencing a housing boom. As a consequence, home buyers were required to borrow core 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 debt.
Estimate with 95% confidence the mean income (INCOME) of Americans in 2012.
Do the data provide enough evidence to infer that the average American adult completed more than 12 years of education (EDUC)?
Estimate with 95% confidence the mean numbers of earners (EARNRS) in the household in 2012.
Can we infer that the mean number of hours worked (HRS1) among those working full or part time is greater than 40?
Is there sufficient evidence to infer that the average American watches more than 24 hours per week, which is 3 hours per day (TVHOURS)?
Can we infer from the data that the average American with children was less than 25 years old when his or her first child was born (AGEKDBRN)?
Estimate with 99% confidence the average total family income (TFINCOME) in 2012.
Can we infer that the Americans have on average less than two children (CHILDS)?
Is there sufficient evidence to conclude that American families with children have on average less than two children (CHILDS)?
Estimate with 95% confidence the average amount of television watched per day (TVHOURS).
Is there sufficient evidence to infer that the average American has more than a high school education, which is more than 12 years of education (EDUC)?
Is there enough evidence to conclude that the average American with children was less than 25 years old when his or her first child was born (AGEKDBRN)?
Can we infer that the average American works more than 40 hours per week (HRS1)?
Estimate with 95% confidence the average American annual income (INCOME).
Estimate with 95% confidence the average American total family annual income (TFINCOME).
Estimate with 99% confidence the average number of earners per household (EARNRS).
Is there enough evidence to conclude that the average household contains less than two adults (ADULTS)?
Can we infer that the average American has completed more than 12 years of education (EDUC)?
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.
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).
a. A random sample of 100 observations was drawn from a normal population. The sample variance was calculated to be s2 = 220. Test with α = .05 to determine whether we can infer that the population variance differs from 300.b. Repeat Part a changing the sample size to 50.c. What is the effect of
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 σ2 is less than 100?b. Repeat part (a) increasing the sample size to 100.c. What is the effect of increasing the sample size?
a. Estimate σ2 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?
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.
After many years of teaching, a statistics professor computed the variance of the marks on her final exam and found it to be Ïƒ2 = 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 sample of
With gasoline prices increasing, drivers are more concerned with their carsâ€™ 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 Ïƒ2 = 23 mpg2. Now that his car is 5 years old, he would like to
During annual checkups physicians routinely send their patients to medical laboratories to have various tests performed. One such test determines the cholesterol level in patientsâ€™ blood. However, not all tests are conducted in the same way. To acquire more information, a man was sent to
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 experienced some inventory problems, which induced

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