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mathematics
statistics

Questions and Answers of Statistics

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
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.
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 =
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
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
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
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
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,
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,
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
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
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
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
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
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
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
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
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
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
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
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 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
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
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
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
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
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
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:
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
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
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
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
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. 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.
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
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
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
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.
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
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
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
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
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. 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
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.
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.
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
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%
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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)
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
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
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.
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

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