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Statistics For Management And Economics Abbreviated 10th Edition Gerald Keller - Solutions
The marks on a statistics midterm test are normally distributed with a mean of 78 and a standard deviation of 6.a. What proportion of the class has a midterm mark of less than 75?b. What is the probability that a class of 50 has an average midterm mark that is less than 75?
The amount of time spent by North American adults watching television per day is normally distributed with a mean of 6 hours and a standard deviation of 1.5 hours.a. What is the probability that a randomly selected North American adult watches television for more than 7 hours per day?b. What is the
The manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with a mean of 6.05 ounces and a standard deviation of .18 ounces. Suppose that you draw a random sample of 36 cans.a. Find the probability that
The number of customers who enter a supermarket each hour is normally distributed with a mean of 600 and a standard deviation of 200. The supermarket is open 16 hours per day. What is the probability that the total number of customers who enter the supermarket in one day is greater than 10,000?
Refer to Exercise. Suppose that the professor discovers that the weights of people who use the elevator are normally distributed with an average of 75 kilograms and a standard deviation of 10 kilograms. Calculate the probability that the professor seeks.In Exercise, the sign on the elevator in the
The time it takes for a statistics professor to mark his midterm test is normally distributed with a mean of 4.8 minutes and a standard deviation of 1.3 minutes.There are 60 students in the professor’s class. What is the probability that he needs more than 5 hours to mark all the midterm tests?
The restaurant in a large commercial building provides coffee for the occupants in the building. The restaurateur has determined that the mean number of cups of coffee consumed in a day by all the occupants is 2.0 with a standard deviation of .6. A new tenant of the building intends to have a
The number of pages produced by a fax machine in a busy office is normally distributed with a mean of 275 and a standard deviation of 75. Determine the probability that in 1 week (5 days) more than 1,500 faxes will be received?
a. In a binomial experiment with n = 300 and p = .5, find the probability that P̂ is greater than 60%.b. Repeat part (a) with p = .55.c. Repeat part (a) with p = .6
a. The probability of success on any trial of a binomial experiment is 25%. Find the probability that the proportion of successes in a sample of 500 is less than 22%.b. Repeat part (a) with n = 800.c. Repeat part (a) with n = 1,000.
Determine the probability that in a sample of 100 the sample proportion is less than .75 if p = .80.
A binomial experiment where p = .4 is conducted. Find the probability that in a sample of 60 the proportion of successes exceeds .35.
The proportion of eligible voters in the next election who will vote for the incumbent is assumed to be 55%. What is the probability that in a random sample of 500 voters less than 49% say they will vote for the incumbent?
The assembly line that produces an electronic component of a missile system has historically resulted in a 2% defective rate. A random sample of 800 components is drawn. What is the probability that the defective rate is greater than 4%? Suppose that in the random sample the defective rate is 4%.
a. The manufacturer of aspirin claims that the proportion of headache sufferers who get relief with just two aspirins is 53%. What is the probability that in a random sample of 400 headache sufferers, less than 50% obtain relief? If 50% of the sample actually obtained relief, what does this suggest
The manager of a restaurant in a commercial building has determined that the proportion of customers who drink tea is 14%. What is the probability that in the next 100 customers at least 10% will be tea drinkers?
A commercial for a manufacturer of household appliances claims that 3% of all its products require a service call in the first year. A consumer protection association wants to check the claim by surveying 400 households that recently purchased one of the company’s appliances. What is the
The Laurier Company’s brand has a market share of 30%. Suppose that 1,000 consumers of the product are asked in a survey which brand they prefer. What is the probability that more than 32% of the respondents say they prefer the Laurier brand?
A university bookstore claims that 50% of its customers are satisfied with the service and prices.a. If this claim is true, what is the probability that in a random sample of 600 customers less than 45% are satisfied?b. Suppose that in a random sample of 600 customers, 270 express satisfaction with
A psychologist believes that 80% of male drivers when lost continue to drive hoping to find the location they seek rather than ask directions. To examine this belief, he took a random sample of 350 male drivers and asked each what they did when lost. If the belief is true, determine the probability
The Red Lobster restaurant chain regularly surveys its customers. On the basis of these surveys, the management of the chain claims that 75% of its customers rate the food as excellent. A consumer testing service wants to examine the claim by asking 460 customers to rate the food. What is
An accounting professor claims that no more than one-quarter of undergraduate business students will major in accounting. What is the probability that in a random sample of 1,200 undergraduate business students, 336 or more will major in accounting?
Independent random samples of 10 observations each are drawn from normal populations. The parameters of these populations arePopulation 1: µ = 280, σ = 25Population 2: µ = 270, σ = 30Find the probability that the mean of sample 1 is greater than the mean of sample 2 by more than 25.
Repeat Exercise 9.45 with samples of size 50.Population 1: µ = 280, σ = 25Population 2: µ = 270, σ = 30
Repeat Exercise 9.45 with samples of size 100.Population 1: µ = 280, σ = 25Population 2: µ = 270, σ = 30
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 population, what is the probability that the mean of sample 1 is greater than the mean of sample 2?Population 1: µ = 40, σ = 6Population 2: µ = 38, σ
Repeat Exercise 9.48 assuming that the standard deviations are 12 and 16, respectively.Population 1: µ = 40, σ = 6Population 2: µ = 38, σ = 8
Repeat Exercise 9.48 assuming that the means are 140 and 138, respectively.Population 1: µ = 40, σ = 6Population 2: µ = 38, σ = 8
A factory’s worker productivity is normally distributed. One worker produces an average of 75 units per day with a standard deviation of 20. Another worker produces at an average rate of 65 per day with a standard deviation of 21. What is the probability that in 1 week (5 working days), worker 1
A professor of statistics noticed that the marks in his course are normally distributed. He has also noticed that his morning classes average 73%, with a standard deviation of 12% on their final exams. His afternoon classes average 77%, with a standard deviation of 10%.What is the probability that
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 the latter is only 15%. If tips are normally
The average North American loses an average of 15 days per year to colds and flu. The natural remedy Echinacea reputedly boosts the immune system. One manufacturer of Echinacea pills claims that consumers of its product will reduce the number of days lost to colds and flu by one-third. To test the
A sample of n = 16 observations is drawn from a normal population with µ = 1,000 and σ = 200. Find the following.a. P (x̄ > 1,050)b. P (x̄ < 960)c. P (x̄ > 1,100)
Repeat Exercise 9.7 with n = 25.A sample of n = 16 observations is drawn from a normal population with µ = 1,000 and σ = 200. Find the following.a. P (x̄ > 1,050)b. P (x̄ < 960)c. P (x̄ > 1,100)
Draw a sampling distribution of an unbiased estimator.
Draw a sampling distribution of a biased estimator.
Draw diagrams representing what happens to the sampling distribution of a consistent estimator when the sample size increases.
Draw a diagram that shows the sampling distribution representing two unbiased estimators, one of which is relatively efficient.
The following data represent a random sample of 9 marks (out of 10) on a statistics quiz. The marks are normally distributed with a standard deviation of 2. Estimate the population mean with 90% confidence.7 9 7 5 4 8 3 10 9
The following observations are the ages of a random sample of 8 men in a bar. It is known that the ages are normally distributed with a standard deviation of 10. Determine the 95% confidence interval estimate of the population mean. Interpret the intervalestimate.
How many rounds of golf do physicians (who play golf) play per year? A survey of 12 physicians revealed the following numbers:Estimate with 95% confidence the mean number of rounds per year played by physicians, assuming that the number of rounds is normally distributed with a standard deviation
Among the most exciting aspects of a university professor’s life are the departmental meetings where such critical issues as the color of the walls will be painted and who gets a new desk are decided. A sample of 20 professors was asked how many hours per year are devoted to these meetings.
The number of cars sold annually by used car salespeople is normally distributed with a standard deviation of 15. A random sample of 15 sales-people was taken, and the number of cars each sold is listed here. Find the 95% confidence interval estimate of the population mean. Interpret the
It is known that the amount of time needed to change the oil on a car is normally distributed with a standard deviation of 5 minutes. The amount of time to complete a random sample of 10 oil changes was recorded and listed here. Compute the 99% confidence interval estimate of the mean of
Suppose that the amount of time teenagers spend weekly working at part-time jobs is normally distributed with a standard deviation of 40 minutes. A random sample of 15 teenagers was drawn, and each reported the amount of time spent at part-time jobs (in minutes). These are listed here. Determine
One of the few negative side effects of quitting smoking is weight gain. Suppose that the weight gain in the 12 months following a cessation in smoking is normally distributed with a standard deviation of 6 pounds. To estimate the mean weight gain, a random sample of 13 quitters was drawn; their
Because of different sales ability, experience, and devotion, the incomes of real estate agents vary considerably. Suppose that in a large city the annual income is normally distributed with a standard deviation of $15,000. A random sample of 16 real estate agents was asked to report their annual
A survey of 400 statistics professors was undertaken. Each professor was asked how much time was devoted to teaching graphical techniques. We believe that the times are normally distributed with a standard deviation of 30 minutes. Estimate the population mean with 95% confidence.
In a survey conducted to determine, among other things, the cost of vacations, 64 individuals were randomly sampled. Each person was asked to compute the cost of her or his most recent vacation. Assuming that the standard deviation is $400, estimate with 95% confidence the average cost of all
In an article about disinflation, various investments were examined. The investments included stocks, bonds, and real estate. Suppose that a random sample of 200 rates of return on real estate investments was computed and recorded. Assuming that the standard deviation of all rates of return on real
A statistics professor is in the process of investigating how many classes university students miss each semester. To help answer this question, she took a random sample of 100 university students and asked each to report how many classes he or she had missed in the previous semester. Estimate the
As part of a project to develop better lawn fertilizers, a research chemist wanted to determine the mean weekly growth rate of Kentucky bluegrass, a common type of grass. A sample of 250 blades of grass was measured, and the amount of growth in 1 week was recorded. Assuming that weekly growth
A time study of a large production facility was undertaken to determine the mean time required to assemble a cell phone. A random sample of the times to assemble 50 cell phones was recorded. An analysis of the assembly times reveals that they are normally distributed with a standard deviation of
The image of the Japanese manager is that of a workaholic with little or no leisure time. In a survey, a random sample of 250 Japanese middle managers was asked how many hours per week they spent in leisure activities (e.g., sports, movies, television). The results of the survey were recorded.
One measure of physical fitness is the amount of time it takes for the pulse rate to return to normal after exercise. A random sample of 100 women age 40 to 50 exercised on stationary bicycles for 30 minutes. The amount of time it took for their pulse rates to return to pre-exercise levels was
A survey of 80 randomly selected companies asked them to report the annual income of their presidents. Assuming that incomes are normally distributed with a standard deviation of $30,000, determine the 90% confidence interval estimate of the mean annual income of all company presidents. Interpret
To help make a decision about expansion plans, the president of a music company needs to know how many compact discs teenagers buy annually. Accordingly, he commissions a survey of 250 teenagers. Each is asked to report how many CDs he or she purchased in the previous 12 months. Estimate with
The sponsors of television shows targeted at the children’s market wanted to know the amount of time children spend watching television because the types and number of programs and commercials are greatly influenced by this information. As a result, it was decided to survey 100 North American
Review Exercise 10.41. Describe what happens to the sample size whena. The population standard deviation increases.b. The confidence level increases.c. The bound on the error of estimation increases.
Review the results of Exercise 10.43. Describe what happens to the sample size whena. The population standard deviation decreases.b. The confidence level decreases.c. The bound on the error of estimation decreases.
a. Determine the sample size necessary to estimate a population mean to within 1 with 90% confidence given that the population standard deviation is 10.b. Suppose that the sample mean was calculated as 150. Estimate the population mean with 90% confidence.
a. Repeat part (b) in Exercise 10.45 after discovering that the population standard deviation is actually 5.b. Repeat part (b) in Exercise 10.45 after discovering that the population standard deviation is actually 20.
Review Exercises 10.45 and 10.46. Describe what happens to the confidence interval estimate whena. The standard deviation is equal to the value used to determine the sample size.b. The standard deviation is smaller than the one used to determine the sample size.c. The standard deviation is larger
a. A statistics practitioner would like to estimate a population mean to within 10 units. The confidence level has been set at 95% and σ = 200. Determine the sample size.b. Suppose that the sample mean was calculated as 500. Estimate the population mean with 95% confidence.
a. Repeat part (b) of Exercise 10.48 after discovering that the population standard deviation is actually 100.b. Repeat part (b) of Exercise 10.48 after discovering that the population standard deviation is actually 400.
Review Exercises 10.48 and 10.49. Describe what happens to the confidence interval estimate whena. The standard deviation is equal to the value used to determine the sample size.b. The standard deviation is smaller than the one used to determine the sample size.c. The standard deviation is larger
a. A statistics practitioner took a random sample of 50 observations from a population with a standard deviation of 25 and computed the sample mean to be 100. Estimate the population mean with 90% confidence.b. Repeat part (a) using a 95% confidence level.c. Repeat part (a) using a 99% confidence
a. The mean of a random sample of 25 observations from a normal population with a standard deviation of 50 is 200. Estimate the population mean with 95% confidence.b. Repeat part (a) changing the population standard deviation to 25.c. Repeat part (a) changing the population standard deviation to
a. A random sample of 25 was drawn from a normal distribution with a standard deviation of 5. The sample mean is 80. Determine the 95% confidence interval estimate of the population mean.b. Repeat part (a) with a sample size of 100.c. Repeat part (a) with a sample size of 400.d. Describe what
a. Given the following information, determine the 98% confidence interval estimate of the population mean:b. Repeat part (a) using a 95% confidence level.c. Repeat part (a) using a 90% confidence level.d. Review parts (a)–(c) and discusses the effect on the confidence interval estimator of
a. The mean of a sample of 25 was calculated as x̄ = 500. The sample was randomly drawn from a population with a standard deviation of 15. Estimate the population mean with 99% confidence.b. Repeat part (a) changing the population standard deviation to 30.c. Repeat part (a) changing the population
a. A statistics practitioner randomly sampled 100 observations from a population with a standard deviation of 5 and found that x̄ is 10. Estimate the population mean with 90% confidence.b. Repeat part (a) with a sample size of 25.c. Repeat part (a) with a sample size of 10.d. Describe what happens
a. From the information given here determine the 95% confidence interval estimate of the population mean.x̄ = 100 σ = 20 n = 25b. Repeat part (a) with x = 200.c. Repeat part (a) with x = 500.d. Describe what happens to the width of the confidence interval estimate when the sample means increases.
a. A random sample of 100 observations was randomly drawn from a population with a standard deviation of 5. The sample mean was calculated as x̄ = 400. Estimate the population mean with 99% confidence.b. Repeat part (a) with x̄ = 200.c. Repeat part (a) with x̄ = 100.d. Describe what happens to
a. Given the following information, determine the 90% confidence interval estimate of the population mean using the sample median. Sample median = 500, σ = 12, and n = 50b. Compare your answer in part (a) to that produced in part (c) of Exercise 10.12. Why is the confidence interval estimate based
a. Determine the sample size required to estimate a population mean to within 10 units given that the population standard deviation is 50. A confidence level of 90% is judged to be appropriate.b. Repeat part (a) changing the standard deviation to 100.c. Re-do part (a) using a 95% confidence
a. A statistics practitioner would like to estimate a population mean to within 50 units with 99% confidence given that the population standard deviation is 250. What sample size should be used?b. Re-do part (a) changing the standard deviation to 50.c. Re-do part (a) using a 95% confidence level.d.
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 plaintiff (the victims’ relatives) are
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 = 1000H1: µ ≠ 1000σ = 200, n = 100, x̄ = 980, α = .01
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 = 50H1: µ > 50σ = 5, n = 9, x̄ = 51, α = .03
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 = 15H1: µ < 15σ = 2, n = 25, x̄ = 14.3, α = .10
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 = 100H1: µ ≠ 100σ = 10, n = 100, x̄ = 100, α = .05
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 = 70H1: µ > 70σ = 20, n = 100, x̄ = 80, α = .01
“What-if analyses” designed to determine what happens to the test statistic and p-value when the sample size, standard deviation, and sample mean change. These problems can be solved manually, using the spreadsheet you created in this section, or by using Minitab.H0: µ = 50H1: µ < 50σ =
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 deviation is 8 minutes.To help reduce the
A low-handicap golfer who uses Titleist brand golf balls observed that his average drive is 230 yards and the standard deviation is 10 yards. Nike has just introduced a new ball, which has been endorsed by Tiger Woods. Nike claims that the ball will travel farther than Titleist. To test the claim,
Calculate the probability of a Type II error for the following test of hypothesis, given that µ = 203.H0: µ = 200H1: µ ≠ 200α = .05, σ = 10, n = 100
Find the probability of a Type II error for the following test of hypothesis, given that µ = 1,050.H0: µ = 1,000H1: µ > 1,000α = .01, σ = 50, n = 25
Determine β for the following test of hypothesis, given that µ = 48.H0: µ = 50H1: µ < 50α = .05, σ = 10, n = 40
For each of Exercises 11.48-11.50, draw the sampling distributions similar to Figure.
A statistics practitioner wants to test the following hypotheses with σ = 20 and n = 100:H0: µ = 100H1: µ > 100a. 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 decreasing α
a. Calculate the probability of a Type II error for the following hypotheses when µ = 37:H0: µ = 40H1: µ < 40The 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 the effect on β of increasing α.
Draw the figures of the sampling distributions for Exercises 11.52 and 11.53.
a. Find the probability of a Type II error for the following test of hypothesis, given that µ = 196:H0: µ = 200H1: µ < 200The significance level is 10%, the population standard deviation is 30, and the sample size is 25.b. Repeat part (a) with n = 100.c. Describe the effect on β of
a. Determine β for the following test of hypothesis, given that µ = 310:H0: µ = 300H1: µ > 300The 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) with n = 36.c. Describe the effect on β of
For Exercises 11.55 and 11.56, draw the sampling distributions similar to Figure 11.9.
For the test of hypothesisH0: µ = 1,000H1: µ ≠ 1,000α = .05, σ = 200Draw the operating characteristic curve for n = 25, 100, and 200.
Draw the operating characteristic curve for n = 10, 50, and 100 for the following test:H0: µ = 400H1: µ > 400α = .05, σ = 50
Suppose that in Example 11.1 we wanted to determine whether there was sufficient evidence to conclude that the new system would not be cost-effective. Set up the null and alternative hypotheses and discuss the consequences of Type I and Type II errors. Conduct the test. Is your conclusion the same
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’s feasibility is a two-stage process. In
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