Exam 10: Two-Sample Tests and One-Way ANOVA

TABLE 10-18 As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles. She took three of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below -Referring to Table 10-18, the test is robust to the violation of the assumption that the population of speeds is normally distributed.

TABLE 10-18 As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles. She took three of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below -Referring to Table 10-18, the null hypothesis should be rejected at a 5% level of significance.

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

A powerful women's group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1)and 40 women (group 2)were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. If the p-value turns out to be 0.035 (which is NOT the real value in this data set), then

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 four 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, there are ________ degrees of freedom for this test.

TABLE 10-15 The table below presents the summary statistics for the starting annual salaries (in thousands of dollars) for individuals entering the public accounting and financial planning professions. Sample 1 (public accounting): 1 = 60.35, S1 = 3.25, n1 = 12 Sample 2 (financial planning): 2 = 58.20, S2 = 2.48, n2 = 14 Test whether the mean starting annual salaries for individuals entering the public accounting professions is higher than that of financial planning, assuming that the two population variances are the same. -Referring to Table 10-15, what is(are)the critical value(s)of the relevant hypothesis test if the level of significance is 0.05?

When testing H₀: π₁ - π₂ = 0 versus H₁: π₁ - π₂ ≠ 0, the observed value of the Z test statistic was found to be -2.13. The p-value for this test is ________.

In testing the difference between two proportions using the normal distribution, you may use a two-tail Z test.

The F test statistic in a one-way ANOVA is

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 p-value of the test statistic is ________.

The sample size in each independent sample must be the same if we are to test for differences between the means of two independent populations.

A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test, and found out that the variances were equal. For this situation, the professor should use a t test with independent samples.

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. The result of the pooled-variance t test of the mean salaries of the females (Population 1) and males (Population 2) in the sample is given below. -Referring to Table 10-2, what is the 99% confidence interval estimate for the difference between two means?

TABLE 10-15 The table below presents the summary statistics for the starting annual salaries (in thousands of dollars) for individuals entering the public accounting and financial planning professions. Sample 1 (public accounting): 1 = 60.35, S1 = 3.25, n1 = 12 Sample 2 (financial planning): 2 = 58.20, S2 = 2.48, n2 = 14 Test whether the mean starting annual salaries for individuals entering the public accounting professions is higher than that of financial planning, assuming that the two population variances are the same. -Referring to Table 10-15, suppose α = 0.10. Which of the following represents the result of the relevant hypothesis test?

TABLE 10-14 The use of preservatives by food processors has become a controversial issue. Suppose two preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below. Preservative I Preservative II I = 106.4 hours II= 96.54 hours SI = 10.3 hours SII = 13.4 hours -Referring to Table 10-14, what is the largest level of significance at which a test of whether the population variances differ for preservatives I and II will not be rejected?

TABLE 10-13 The amount of time required to reach a customer service representative has a huge impact on customer satisfaction. Below is the Microsoft 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 largest level of significance at which a test on a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels will not be rejected?

TABLE 10-18 As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles. She took three of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below -Referring to Table 10-18, the sporting goods retailer decided to perform an ANOVA F test. The amount of total variation or SST is ________.

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 = 1,050 -Referring to Table 10-3, suppose α = 0.10. Which of the following represents the correct conclusion?

TABLE 10-20 A hotel chain has identically sized resorts in five locations. The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the five locations. -Referring to Table 10-20, what are the numerator and denominator degrees of freedom for Levene's test for homogeneity of variances respectively?

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, a two-tail test of the null hypothesis of no difference would ________ (be rejected/not be rejected)at the α = 0.05 level of significance.