Exam 10: Two-Sample Tests

TABLE 10-9 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: $n = 109 , p _ { M } = 0.422018 \quad$ Females: $n = 52 , p _ { F } = 0.25$ $p M - p F = 0.172018\quad \quad \quad \quad \quad Z = 211825$ -Referring to Table 10-9, suppose Pepsi wanted to test to determine if the males preferred Pepsi less than the females. Using the test statistic given, compute the appropriate p-value for the test.

$\text { TABLE 10-11 }$ 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 ×and × 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 10-11, the company tests to determine at the 0.05 level whether the population proportion has changed from the previous study. Which of the following is most correct?

TABLE 10-6 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 10-6, the p-value for a two-tailed test whose computed t statistic is 2.50 is between____ and____ .

TABLE 10-13 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 10-13, construct a 99% confidence interval estimate of the difference in proportion between the Kohler and Russell disks that are defective.

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. Exam Score Exam Score Student Before Course (1) After Course (2) 1 530 670 2 690 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 -Referring to Table 10-5, in examining the differences between related samples we are essentially sampling from an underlying population of difference "scores."

TABLE 10-12 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 10-12, the value of the test statistic is _______.

When testing H₀ : µ₁ - µ₂ = 0 versus H₁ : µ₁ - µ₂ × 0, the observed value of the Z-score was found to be - 2.13. The p-value for this test would be

Moving companies are required by the government to publish a Carrier Performance Report each year. One of the descriptive statistics they must include is the annual percentage of shipments on which a $50 or greater claim for loss or damage was filed. Suppose two companies, Econo-Move and On-the-Move, each decide to estimate this figure by sampling their records, and they report the data shown in the following table. The owner of On-the-Move is hoping to use these data to show that the company is superior to Econo-Move with regard to the percentage of claims filed. Which test would be used to properly analyze the data in this experiment? E cono- Move On-the- Move Total shipments sampled 900 750 Number of shipments with a claim c \ 50 162 60

If we wish to determine whether there is evidence that the proportion of items of interest is higher in group 1 than in group 2, the appropriate test to use is

A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training. To test whether any improvement occurred, the instructor would use a t-distribution with 11 degrees of freedom.

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.

The test for the equality of 2 population variances assumes that each of the two populations is normally distributed.

TABLE 10-14 A problem with a telephone line that prevents a customer from receiving or making calls is disconcerting to both the customer and the telephone company. The data on samples of 20 problems reported to twodifferent offices of a telephone company and the time toclear these problems (in minutes) from the customers'lines are collected. Belowis the Excel output to see whether there is evidence of a difference in the mean waitingtime between the two offices assuming that the population variances in the two offices are not equal. $\text { t-Test: Two- Sample Assuming Unequal Variances }$ Office 1 Office 2 Mean 2214 2.0115 Variance 2.951657 3.57855 Observations 20 20 Hypothesized Mean Difference 0 38 Stat 0.354386 (<=) one- tail 0.362504 Critical one- tail 1.685953 (<=) two- tail 0.725009 Critical two-tail 2.024394 -Referring to Table 10-14, what is the largest level of significance at which a test on a difference in the variability of the waiting time between the two offices will not be rejected?

TABLE 10-2 A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below. -Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. From the analysis in Table 10-2, the correct test statistic is

In testing for differences between the means of two related populations, the null hypothesis is

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

TABLE 10-12 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 10-12, construct a 90% confidence interval estimate of the difference in proportion between accounting majors and economic majors who have a job offer on graduation day.

Repeated measurements from the same individuals is an example of data collected from two related populations.

TABLE 10-14 A problem with a telephone line that prevents a customer from receiving or making calls is disconcerting to both the customer and the telephone company. The data on samples of 20 problems reported to two different offices of a telephone company and the time to clear these problems (in minutes) from the customers' lines are collected. Below is the Excel output to see whether there is evidence of a difference in the mean waiting time between the two offices assuming that the population variances in the two offices are not equal. t- Test: Two- Sample Assuming Unequal Variances Office 1 Office 2 Mean 2214 2.0115 Variance 2.951657 3.57855 Observations 20 20 Hypothesized Mean Difference 0 38 Stat 0.354386 (<=) one- tail 0.362504 Critical one- tail 1.685953 (<=) two- tail 0.725009 Critical two-tail 2.024394 -Referring to Table 10-14, suppose ? = 0.05. Which of the following represents the correct conclusion?

TABLE 10-4 A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. 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: $\overline{X}$ _G = 35 months, s_G² = 900 $\quad$ $\quad$ Metropolis: $\overline{X}$ _M = 50 months, s_M² = 1050 -Referring to Table 10-4, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.01?