Exam 10: Two-Sample Tests

When you test for differences between the means of two independent populations,you can only use a two-tail test.

The test for the equality of two population variances is based on

TABLE 10-12 A quality control engineer is in charge of the manufacture of computer disks.Two different processes can be used to manufacture the disks.He suspects that the Kohler method produces a greater proportion of defects than the Russell method.He samples 150 of the Kohler and 200 of the Russell disks and finds that 27 and 18 of them,respectively,are defective.If Kohler is designated as "Group 1" and Russell is designated as "Group 2," perform the appropriate test at a level of significance of 0.01. -Referring to Table 10-12,construct a 90% confidence interval estimate of the difference in proportion between the Kohler and Russell disks that are defective.

The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women.The article claimed that women perceived the problem to be much more prevalent than did men.One question asked to both men and women was: "Do you think sexual harassment is a major problem in the American workplace?" Some 24% of the men compared to 62% of the women responded "Yes." Suppose that 150 women and 200 men were interviewed.What is the value of the test statistic?

TABLE 10-3 A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes. Gotham: G = 35 months, SG² = 900 Metropolis: M = 50 months,SM² = 1050 -Referring to Table 10-3,what is the 95% confidence interval estimate for the difference in the two means?

TABLE 10-4 Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances.The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0. -Referring to Table 10-4,the pooled (i.e.,combined)variance is ________.

TABLE 10-8 A few years ago,Pepsi invited consumers to take the "Pepsi Challenge." Consumers were asked to decide which of two sodas,Coke or Pepsi,they preferred in a blind taste test.Pepsi was interested in determining what factors played a role in people's taste preferences.One of the factors studied was the gender of the consumer.Below are the results of analyses comparing the taste preferences of men and women with the proportions depicting preference for Pepsi. Males: n = 109,pM = 0.422018 Females: n = 52,pF = 0.25 pM - pF = 0.172018 Z = 2.11825 -Referring to Table 10-8,construct a 99% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

TABLE 10-8 A few years ago,Pepsi invited consumers to take the "Pepsi Challenge." Consumers were asked to decide which of two sodas,Coke or Pepsi,they preferred in a blind taste test.Pepsi was interested in determining what factors played a role in people's taste preferences.One of the factors studied was the gender of the consumer.Below are the results of analyses comparing the taste preferences of men and women with the proportions depicting preference for Pepsi. Males: n = 109,pM = 0.422018 Females: n = 52,pF = 0.25 pM - pF = 0.172018 Z = 2.11825 -Referring to Table 10-8,construct a 95% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

TABLE 10-11 The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day.He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors.In a random sample of 100 of each type of major at graduation,he found that 65 accounting majors and 52 economics majors had job offers.If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05. -Referring to Table 10-11,the same decision would be made with this test if the level of significance had been 0.01 rather than 0.05.

TABLE 10-5 To test the effectiveness of a business school preparation course,8 students took a general business test before and after the course.The results are given below. -Referring to Table 10-5,in examining the differences between related samples we are essentially sampling from an underlying population of difference "scores."

The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women.The article claimed that women perceived the problem to be much more prevalent than did men.One question asked to both men and women was: "Do you think sexual harassment is a major problem in the American workplace?" Some 24% of the men compared to 62% of the women responded "Yes." Suppose that 150 women and 200 men were interviewed.Construct a 95% confidence interval estimate of the difference between the proportion of women and men who think sexual harassment is a major problem in the American workplace.

TABLE 10-5 To test the effectiveness of a business school preparation course,8 students took a general business test before and after the course.The results are given below. -Referring to Table 10-5,what is the critical value for testing at the 5% level of significance whether the business school preparation course is effective in improving exam scores?

TABLE 10-13 The amount of time required to reach a customer service representative has a huge impact on customer satisfaction.Below is the Excel output from a study to see whether there is evidence of a difference in the mean amounts of time required to reach a customer service representative between two hotels.Assume that the population variances in the amount of time for the two hotels are not equal. -Referring to Table 10-13,what is the standardized value of the estimate of the mean of the sampling distribution for the difference between sample means?

TABLE 10-6 To investigate the efficacy of a diet,a random sample of 16 male patients is selected from a population of adult males using the diet.The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later.Assuming that the population of differences in weight before versus after the diet follow a normal distribution,the t test for related samples can be used to determine if there was a significant decrease in the mean weight during this period.Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds. -Referring to Table 10-6,a one-tail test of the null hypothesis of no difference would ________ (be rejected/not be rejected)at the α = 0.05 level of significance.

The F distribution can only have positive values.

TABLE 10-10 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course.The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course.The groups are assumed to be independent random samples.Let π₁ and π₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study,respectively. -Referring to Table 10-10,construct a 99% confidence interval estimate of the difference in proportion of workers who would like to attend a self-improvement course in the recent study and the past study.

TABLE 10-4 Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances.The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0. -Referring to Table 10-4,what is the 95% confidence interval estimate for the difference in the two means?

TABLE 10-4 Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances.The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0. -Referring to Table 10-4,what is the 99% confidence interval estimate for the difference in the two means?

TABLE 10-3 A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes. Gotham: G = 35 months, SG² = 900 Metropolis: M = 50 months,SM² = 1050 -Referring to Table 10-3,what is the test statistic for the difference between sample means?

TABLE 10-7 A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging.In order to determine if his suspicion is correct,he contacts a second supplier and asks for the prices on various identical materials.He wants to compare these prices with those of his primary supplier.The data collected is presented in the table below,with some summary statistics presented (all of these might not be necessary to answer the questions which follow).The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01. -Referring to Table 10-7,the calculated value of the test statistic is ________.