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Introductory Statistics 8th Edition Prem S. Mann - Solutions

Consider the null hypothesis H0: µ = 12.80. A random sample of 58 observations is taken from this population to perform this test. Using α = .05, show the rejection and non-rejection regions on the sampling distribution curve of the sample mean and find the critical value(s) of t for the
Consider H0: µ = 80 versus H1: µ ≠ 80 for a population that is normally distributed. a. A random sample of 25 observations taken from this population produced a sample mean of 77 and a standard deviation of 8. Using α = .01, would you reject the null hypothesis? b. Another random sample of 25
Consider H0: µ = 40 versus H1: µ > 40. a. A random sample of 64 observations taken from this population produced a sample mean of 43 and a standard deviation of 5. Using α = .025, would you reject the null hypothesis? b. Another random sample of 64 observations taken from the same population
Perform the following tests of hypothesis. a. H0: µ = 285, H1: µ ≠ 285 n = 55, = 267.80, s = 42.90, α = .05 b. H0: µ = 10.70, H1: µ ≠ 10.70, n = 47, = 12.025, s = 4.90, α = .01 c. H0: µ = 147,500, H1: µ ≠ 147,500, n = 41, = 149,812, s = 22,972, α = .10
Perform the following tests of hypotheses for data coming from a normal distribution. a. H0: µ = 94.80, H1: µ ≠ 94.80 n = 12, = 92.87, s = 5.34, α = .10 b. H0: µ = 18.70, H1: µ ≠ 18.70, n = 25, = 20.05, s = 2.99, α = .05 c. H0: µ = 59, H1: µ ≠ 59, n = 7, = 59.42, s = .418, α =
The police that patrol a heavily traveled highway claim that the average driver exceeds the 65 miles per hour speed limit by more than 10 miles per hour. Seventy-two randomly selected cars were clocked by airplane radar. The average speed was 77.40 miles per hour, and the standard deviation of the
According to an estimate, the average age at first marriage for women in the United States was 26.1 years in 2010 (Time, March 21, 2011). A recent sample of 60 women from New Jersey who got married for the first time this year showed that their average age at first marriage was 27.2 years with a
The president of a university claims that the mean time spent partying by all students at this university is not more than 7 hours per week. A random sample of 40 students taken from this university showed that they spent an average of 9.50 hours partying the previous week with a standard deviation
The mean balance of all checking accounts at a bank on December 31, 2011, was $850. A random sample of 55 checking accounts taken recently from this bank gave a mean balance of $780 with a standard deviation of $230. Using a 1% significance level, can you conclude that the mean balance of such
A soft-drink manufacturer claims that its 12-ounce cans do not contain, on average, more than 30 calories. A random sample of 64 cans of this soft drink, which were checked for calories, contained a mean of 32 calories with a standard deviation of 3 calories. Does the sample information support the
According to an estimate, the average price of homes in Martha’s Vineyard, Massachusetts, was $650,000 in 2011 (USA TODAY, August 11, 2011). A recent random sample of 70 homes from Martha’s Vineyard showed that their average price is $674,000 with a standard deviation of $94,500. Using a 2%
A paint manufacturing company claims that the mean drying time for its paints is not longer than 45 minutes. A random sample of 20 gallons of paints selected from the production line of this company showed that the mean drying time for this sample is 49.50 minutes with a standard deviation of 3
The manager of a restaurant in a large city claims that waiters working in all restaurants in his city earn an average of $150 or more in tips per week. A random sample of 25 waiters selected from restaurants of this city yielded a mean of $139 in tips per week with a standard deviation of $28.
A business school claims that students who complete a 3-month typing course can type, on average, at least 1200 words an hour. A random sample of 25 students who completed this course typed, on average, 1125 words an hour with a standard deviation of 85 words. Assume that the typing speeds for all
According to an estimate, 2 years ago the average age of all CEOs of medium-sized companies in the United States was 58 years. Jennifer wants to check if this is still true. She took a random sample of 70 such CEOs and found their mean age to be 55 years with a standard deviation of 6 years. a.
A past study claimed that adults in America spent an average of 18 hours a week on leisure activities. A researcher wanted to test this claim. She took a sample of 12 adults and asked them about the time they spend per week on leisure activities. Their responses (in hours) are as follows.Assume
The past records of a supermarket show that its customers spend an average of $95 per visit at this store. Recently the management of the store initiated a promotional campaign according to which each customer receives points based on the total money spent at the store, and these points can be used
According to the Kaiser Family Foundation, U.S. workers who had employer-provided health insurance paid an average premium of $4129 for family health insurance coverage during 2011 (USA TODAY, October 10, 2011). Suppose a recent random sample of 25 workers with employer-provided health insurance
According to an estimate, the average total parent and student debt for new college graduates was $34,400 in 2010–11 (Time, October 31, 2011). A random sample of 500 of this year’s graduates showed that their average such debt is $38,460 with a standard deviation of $5600. Do the data provide
The manager of a service station claims that the mean amount spent on gas by its customers is $15.90 per visit. You want to test if the mean amount spent on gas at this station is different from $15.90 per visit. Briefly explain how you would conduct this test when is not known.
A tool manufacturing company claims that its top-of-the-line machine that is used to manufacture bolts produces an average of 88 or more bolts per hour. A company that is interested in buying this machine wants to check this claim. Suppose you are asked to conduct this test. Briefly explain how you
Explain when a sample is large enough to use the normal distribution to make a test of hypothesis about the population proportion.
In each of the following cases, do you think the sample size is large enough to use the normal distribution to make a test of hypothesis about the population proportion? Explain why or why not. a. n = 40 and p = .11 b. n = 100 and p = .73 c. n = 80 and p = .05 d. n = 50 and p = .14
In each of the following cases, do you think the sample size is large enough to use the normal distribution to make a test of hypothesis about the population proportion? Explain why or why not. a. n = 30 and p = .65 b. n = 70 and p = .05 c. n = 60 and p = .06 d. n = 900 and p = .17
For each of the following examples of tests of hypothesis about the population proportion, show the rejection and non-rejection regions on the graph of the sampling distribution of the sample proportion. a. A two-tailed test with α = .10 b. A left-tailed test with α = .01 c. A right-tailed test
For each of the following examples of tests of hypothesis about the population proportion, show the rejection and non-rejection regions on the graph of the sampling distribution of the sample proportion. a. A two-tailed test with α = .05 b. A left-tailed test with α = .02 c. A right-tailed test
A random sample of 500 observations produced a sample proportion equal to .38. Find the critical and observed values of z for each of the following tests of hypotheses using .05. a. H0: p = .30 versus H1: p > .30 b. H0: p = .30 versus H1: p ≠ .30
A random sample of 200 observations produced a sample proportion equal to .60. Find the critical and observed values of z for each of the following tests of hypotheses using α = .01. a. H0: p = .63 versus H1: p < .63 b. H0: p = .63 versus H1: p ≠ .63
Consider the null hypothesis H0: p = .65. Suppose a random sample of 1000 observations is taken to perform this test about the population proportion. Using α = .05, show the rejection and non-rejection regions and find the critical value(s) of z for a a. Left-tailed test b. Two-tailed test c.
Consider the null hypothesis H0: p = .25. Suppose a random sample of 400 observations is taken to perform this test about the population proportion. Using α = .01, show the rejection and non rejection regions and find the critical value(s) of z for a a. Left-tailed test b. Two-tailed test c.
Consider H0: p = .70 versus H1: p ≠ .70. a. A random sample of 600 observations produced a sample proportion equal to .68. Using α = .01, would you reject the null hypothesis? b. Another random sample of 600 observations taken from the same population produced a sample proportion equal to .76.
Consider H0: p = .45 versus H1: p < .45. a. A random sample of 400 observations produced a sample proportion equal to .42. Using α = .025, would you reject the null hypothesis? b. Another random sample of 400 observations taken from the same population produced a sample proportion of .39. Using α
Make the following hypothesis tests about p. a. H0: p = .45, H1: p = .45, n = 100, p̂ = .49, α = .10 b. H0: p = .72, H1: p = .72, n = 700, p̂ = .64, α = .05 c. H0: p = .30, H1: µ ≠ .30, n = 200, p̂ = .33, α = .01
Make the following hypothesis tests about p. a. H0: p = .57, H1: p = .57, n = 800, p̂ = .50, α = .05 b. H0: p = .26, H1: p = .26, n = 400, p̂ = .23, α = .01 c. H0: p = .84, H1: µ ≠ .84, n = 250, p̂ = .85, α = .025
According to the U.S. Census Bureau, 11% of children in the United States lived with at least one grandparent in 2009 (USA TODAY, June 30, 2011). Suppose that in a recent sample of 1600 children, 224 were found to be living with at least one grandparent. At a 5% significance level, can you conclude
According to a book published in 2011, 45% of the undergraduate students in the United States show almost no gain in learning in their first 2 years of college (Richard Arum et al., Academically Adrift, University of Chicago Press, Chicago, 2011). A recent sample of 1500 undergraduate students
According to a New York Times/CBS News poll conducted during June 24–28, 2011, 55% of the American adults polled said that owning a home is a very important part of the American Dream (The New York Times, June 30, 2011). Suppose this result was true for the population of all American adults in
Write the null and alternative hypotheses for each of the following examples. Determine if each is a case of a two-tailed, a left-tailed, or a right-tailed test. a. To test if the mean number of hours spent working per week by college students who hold jobs is different from 20 hours b. To test
Beginning in the second half of 2011, there were widespread protests in many American cities that were primarily against Wall Street corruption and the increasing gap between the rich and the poor in America. According to a Time Magazine/ABT SRBI poll conducted by telephone during October 9–10,
According to a Pew Research Center nationwide telephone survey of American adults conducted by phone between March 15 and April 24, 2011, 75% of adults said that college education has become too expensive for most people and they cannot afford it (Time, May 30, 2011). Suppose that this result is
According to a Pew Research Center nationwide telephone survey conducted between March 15 and April 24, 2011, 55% of college graduates said that college education prepared them for a job (Time, May 30, 2011). Suppose this result was true of all college graduates at that time. In a recent sample of
A food company is planning to market a new type of frozen yogurt. However, before marketing this yogurt, the company wants to find what percentage of the people like it. The company’s management has decided that it will market this yogurt only if at least 35% of the people like it. The
A mail-order company claims that at least 60% of all orders are mailed within 48 hours. From time to time the quality control department at the company checks if this promise is fulfilled. Recently the quality control department at this company took a sample of 400 orders and found that 208 of them
Brooklyn Corporation manufactures DVDs. The machine that is used to make these DVDs is known to produce not more than 5% defective DVDs. The quality control inspector selects a sample of 200 DVDs each week and inspects them for being good or defective. Using the sample proportion, the quality
Shulman Steel Corporation makes bearings that are supplied to other companies. One of the machines makes bearings that are supposed to have a diameter of 4 inches. The bearings that have a diameter of either more or less than 4 inches are considered defective and are discarded. When working
Two years ago, 75% of the customers of a bank said that they were satisfied with the services provided by the bank. The manager of the bank wants to know if this percentage of satisfied customers has changed since then. She assigns this responsibility to you. Briefly explain how you would conduct
A study claims that 65% of students at all colleges and universities hold off-campus (part-time or fulltime) jobs. You want to check if the percentage of students at your school who hold off-campus jobs is different from 65%. Briefly explain how you would conduct such a test. Collect data from 40
Consider the following null and alternative hypotheses: Ho: µ = 120 versus H1: µ > 120 A random sample of 81 observations taken from this population produced a sample mean of 123.5. The population standard deviation is known to be 15. a. If this test is made at a 2.5% significance level, would
Multiple choice questions: 1. A test of hypothesis is always about a. A population parameter b. A sample statistic c. A test statistic 2. A Type I error is committed when a. A null hypothesis is not rejected when it is actually false b. A null hypothesis is rejected when it is actually true c. An
According to the Kaiser Family Foundation, U.S. workers who had employer-provided health insurance paid an average premium of $921 for single (one person) health insurance coverage during 2011 (USA TODAY, October 10, 2011). Suppose that a recent random sample of 100 workers with employer provided
A minor league baseball executive has become concerned about the slow pace of games played in her league, fearing that it will lower attendance. She meets with the league’s managers and umpires and discusses guidelines for speeding up the games. Before the meeting, the mean duration of
An editor of a New York publishing company claims that the mean time taken to write a textbook is at least 31 months. A sample of 16 textbook authors found that the mean time taken by them to write a textbook was 25 months with a standard deviation of 7.2 months. a. Using a 2.5% significance level,
A financial advisor claims that less than 50% of adults in the United States have a will. A random sample of 1000 adults showed that 450 of them have a will. a. At a 5% significance level, can you conclude that the percentage of people who have a will is less than 50%? b. What is the Type I error
Multiple choice questions: 9. The value of 1 – β gives the a. Probability of committing a Type I error b. Probability of committing a Type II error c. Power of the test 10. A two-tailed test is a test with a. Two rejection regions b. Two non-rejection regions c. Two test statistics 11. A
Briefly explain the meaning of independent and dependent samples. Give one example of each.
The U.S. Department of Labor collects data on unemployment insurance payments made to unemployed people in different states. Suppose that during 2011 a random sample of 1000 unemployed people in Florida received an average weekly unemployment benefit of $219.65, while a random sample of 900
We wish to estimate the difference between the mean scores on a standardized test of students taught by Instructors A and B. The scores of all students taught by Instructor A have a normal distribution with a standard deviation of 15, and the scores of all students taught by Instructor B have a
The weekly weight losses of all dieters on Diet I have a normal distribution with a mean of 1.3 pounds and a standard deviation of .4 pound. The weekly weight losses of all dieters on Diet II have a normal distribution with a mean of 1.5 pounds and a standard deviation of .7 pound. A random sample
Sixty-five percent of all male voters and 40% of all female voters favor a particular candidate. A sample of 100 male voters and another sample of 100 female voters will be polled. What is the probability that at least 10 more male voters than female voters will favor this candidate?
A local college cafeteria has a self-service soft ice cream machine. The cafeteria provides bowls that can hold up to 16 ounces of ice cream. The food service manager is interested in comparing the average amount of ice cream dispensed by male students to the average amount dispensed by female
Employees of a large corporation are concerned about the declining quality of medical services provided by their group health insurance. A random sample of 100 office visits by employees of this corporation to primary care physicians during 2004 found that the doctors spent an average of 19 minutes
A car magazine is comparing the total repair costs incurred during the first three years on two sports cars, the T-999 and the XPY. Random samples of 45 T-999s and 51 XPYs are taken. All 96 cars are 3 years old and have similar mileages. The mean of repair costs for the 45 T-999 cars is $3300 for
The management at New Century Bank claims that the mean waiting time for all customers at its branches is less than that at the Public Bank, which is its main competitor. A business consulting firm took a sample of 200 customers from the New Century Bank and found that they waited an average of 4.5
Maine Mountain Dairy claims that its 8-ounce low-fat yogurt cups contain, on average, fewer calories than the 8-ounce low-fat yogurt cups produced by a competitor. A consumer agency wanted to check this claim. A sample of 27 such yogurt cups produced by this company showed that they contained an
Explain what conditions must hold true to use the t distribution to make a confidence interval and to test a hypothesis about µ1 – µ2 for two independent samples selected from two populations with unknown but equal standard deviations.
The following information was obtained from two independent samples selected from two normally distributed populations with unknown but equal standard deviations. n1 = 21 1 = 13.97 s1 = 3.78 n2 = 20 2 = 15.55 s1 = 3.26 a. What is the point estimate of µ1 – µ2? b. Construct a 95% confidence
The following information was obtained from two independent samples selected from two populations with unknown but equal standard deviations. n1 = 55 1 = 90.740 s1 = 11.60 n2 = 50 2 = 86.30 s1 = 10.25 a. What is the point estimate of µ1 – µ2? b. Construct a 99% confidence interval for µ1 –
Refer to the information given in Exercise 10.17. Test at a 5% significance level if the two population means are different. n1 = 21 1 = 13.97 s1 = 3.78 n2 = 20 2 = 15.55 s1 = 3.26
Describe the sampling distribution of 1 – 2 for two independent samples when σ1 and σ2 are known and either both sample sizes are large or both populations are normally distributed. What are the mean and standard deviation of this sampling distribution?
Refer to the information given in Exercise 10.18. Test at a 1% significance level if the two population means are different n1 = 55 1 = 90.740 s1 = 11.60 n2 = 50 2 = 86.30 s1 = 10.25
Refer to the information given in Exercise 10.17. Test at a 1% significance level if µ1 is less than µ2. n1 = 21 1 = 13.97 s1 = 3.78 n2 = 20 2 = 15.55 s1 = 3.26
Refer to the information given in Exercise 10.18. Test at a 5% significance level if µ1 is greater than µ2. n1 = 55 1 = 90.740 s1 = 11.60 n2 = 50 2 = 86.30 s1 = 10.25
The following information was obtained from two independent samples selected from two normally distributed populations with unknown but equal standard deviations.a. Let 1 be the mean of population 1 and 2 be the mean of population 2. What is the point estimate of µ1 €“ µ2? b.
The following information was obtained from two independent samples selected from two normally distributed populations with unknown but equal standard deviations.a. Let µ1 be the mean of population 1 and 2 be the mean of population 2. What is the point estimate of µ1 €“
The standard recommendation for automobile oil changes is once every 3000 miles. A local mechanic is interested in determining whether people who drive more expensive cars are more likely to follow the recommendation. Independent random samples of 45 customers who drive luxury cars and 40 customers
A town that recently started a single-stream recycling program provided 60-gallon recycling bins to 25 randomly selected households and 75-gallon recycling bins to 22 randomly selected households. The total volume of recycling over a 10-week period was measured for each of the households. The
An insurance company wants to know if the average speed at which men drive cars is greater than that of women drivers. The company took a random sample of 27 cars driven by men on a highway and found the mean speed to be 72 miles per hour with a standard deviation of 2.2 miles per hour. Another
A high school counselor wanted to know if tenth-graders at her high school tend to have more free time than the twelfth-graders. She took random samples of 25 tenth-graders and 23 twelfth-graders. Each student was asked to record the amount of free time he or she had in a typical week. The mean for
A company claims that its medicine, Brand A, provides faster relief from pain than another company€™s medicine, Brand B. A researcher tested both brands of medicine on two groups of randomly selected patients. The results of the test are given in the following table. The mean and standard
The following information is obtained from two independent samples selected from two normally distributed populations. n1 = 18 1 = 7.82 σ1 = 2.35 n2 = 15 2 = 5.99 σ1 = 3.17 a. What is the point estimate of µ1 – µ2? b. Construct a 99% confidence interval for µ1 – µ2. Find the margin of
A consumer organization tested two paper shredders, the Piranha and the Crocodile, designed for home use. Each of 10 randomly selected volunteers shredded 100 sheets of paper with the Piranha, and then another sample of 10 randomly selected volunteers each shredded 100 sheets with the Crocodile.
Quadro Corporation has two supermarket stores in a city. The company’s quality control department wanted to check if the customers are equally satisfied with the service provided at these two stores. A sample of 380 customers selected from Supermarket I produced a mean satisfaction index of 7.6
According to the credit rating agency Equifax, credit limits on newly issued credit cards increased between January 2011 and May 2011 (money.cnn.com/2011/08/19/pf/credit_card_issuance/index.htm). Suppose that random samples of 400 credit cards issued in January 2011 and 500 credit cards issued in
Assuming that the two populations are normally distributed with unequal and unknown population standard deviations, construct a 95% confidence interval for µ1 – µ2 for the following. n1 = 14 1 = 109.43 s1 = 2.26 n2 = 15 2 = 113.88 s1 = 5.84
Assuming that the two populations have unequal and unknown population standard deviations, construct a 99% confidence interval for µ1 – µ2 for the following. n1 = 48 1 = .863 s1 = .176 n2 = 46 2 = .796 s1 = .068
Refer to Exercise 10.33. Test at a 5% significance level if the two population means are different. n1 = 14 1 = 109.43 s1 = 2.26 n2 = 15 2 = 113.88 s1 = 5.84
Refer to Exercise 10.34. Test at a 1% significance level if the two population means are different. n1 = 48 1 = .863 s1 = .176 n2 = 46 2 = .796 s1 = .068
Refer to Exercise 10.33. Test at a 1% significance level if µ1 is less than µ2. n1 = 14 1 = 109.43 s1 = 2.26 n2 = 15 2 = 113.88 s1 = 5.84
Refer to Exercise 10.34. Test at a 2.5% significance level if µ1 is greater than µ2. n1 = 48 1 = .863 s1 = .176 n2 = 46 2 = .796 s1 = .068
According to the information given in Exercise 10.25, a sample of 45 customers who drive luxury cars showed that their average distance driven between oil changes was 3187 miles with a sample standard deviation of 42.40 miles. Another sample of 40 customers who drive compact lower-price cars
The following information is obtained from two independent samples selected from two populations. n1 = 650 1 = 1.05 σ1 = 5.22 n2 = 675 2 = 1.54 σ1 = 6.80 a. What is the point estimate of µ1 – µ2? b. Construct a 95% confidence interval for µ1 – µ2. Find the margin of error for this
As mentioned in Exercise 10.26, a town that recently started a single-stream recycling program provided 60-gallon recycling bins to 25 randomly selected households and 75-gallon recycling bins to 22 randomly selected households. The average total volumes of recycling over a 10-week period were 382
According to Exercise 10.27, an insurance company wants to know if the average speed at which men drive cars is higher than that of women drivers. The company took a random sample of 27 cars driven by men on a highway and found the mean speed to be 72 miles per hour with a standard deviation of 2.2
Refer to Exercise 10.28. Now assume that the two populations are normally distributed with unequal and unknown population standard deviations. In Exercise 28 a. Make a 90% confidence interval for the difference between the corresponding population means. b. Test at a 5% significance level whether
As mentioned in Exercise 10.29, a company claims that its medicine, Brand A, provides faster relief from pain than another company€™s medicine, Brand B. A researcher tested both brands of medicine on two groups of randomly selected patients. The results of the test are given in the
Refer to Exercise 10.30. Now assume that the shredding times for both paper shredders are normally distributed with unequal and unknown standard deviations. a. Construct a 99% confidence interval for the difference between the two population means. b. Using a 1% significance level, can you conclude
As mentioned in Exercise 10.31, Quadro Corporation has two supermarkets in a city. The company’s quality control department wanted to check if the customers are equally satisfied with the service provided at these two stores. A sample of 380 customers selected from Supermarket I produced a mean
Refer to Exercise 10.32. As mentioned in that exercise, according to the credit rating agency Equifax, credit limits on newly issued credit cards increased between January 2011 and May 2011. Suppose that random samples of 400 new credit cards issued in January 2011 and 500 new credit cards issued
Explain when would you use the paired-samples procedure to make confidence intervals and test hypotheses.
Find the following confidence intervals for d, assuming that the populations of paired differences are normally distributed. a. n = 11, = 25.4, sd = 13.5, confidence level = 99% b. n = 23, = 13.2, sd = 4.8, confidence level = 95% c. n = 18, = 34.6, sd = 11.7, confidence level = 90%

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