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

TABLE 10-17 A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below. A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3 B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7 Interpret the results of the analysis summarized in the following table: -Referring to Table 10-17, the null hypothesis for Levene's test for homogeneity of variances is

When the F test is used for ANOVA, the rejection region is always in the right tail.

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 ________.

An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4)are commercially available. The airline will choose the package that bumps the fewest mean number of passengers as possible during a month. An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the experiment.)The number of passengers bumped each week is given below. How should the data be analyzed? Package 1: 12, 14, 9, 11, 16 Package 2: 2, 4, 7, 3, 1 Package 3: 10, 9, 6, 10, 12 Package 4: 7, 6, 6, 15, 12

TABLE 10-19 An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields, 5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a completely randomized design, the results are presented in the table that follows. -Referring to Table 10-19, based on the Tukey-Kramer procedure with an overall level of significance of 0.01, the agronomist would decide that there is a significant difference between the crop yield of Smith and Walsh seeds.

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?" 24% of the men compared to 62% of the women responded "Yes." Suppose that 150 women and 200 men were interviewed. Construct a 90% 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 10-6 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, the t test should be ________-tail.

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 result of the relevant hypothesis test?

TABLE 10-17 A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below. A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3 B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7 Interpret the results of the analysis summarized in the following table: -Referring to Table 10-17, the numerator and denominator degrees of freedom for Levene's test for homogeneity of variances at a 5% level of significance are, respectively,

A researcher is curious about the effect of sleep on students' test performances. He chooses 60 students and gives each two tests: one given after two hours of sleep and one after eight hours of sleep. The test the researcher should use would be a related samples test.

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, what should be the conclusion for the Levene's test for homogeneity of variances at a 5% level of significance?

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 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, the total mean squares is 261.90.

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 ________.

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, which of the following represents the relevant hypotheses to test whether there is evidence of a difference in the mean amounts of time required to reach a customer service representative between two hotels?

TABLE 10-19 An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields, 5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a completely randomized design, the results are presented in the table that follows. -Referring to Table 10-19, the null hypothesis will be rejected at a level of significance of 0.01 if the value of the test statistic is greater than ________.

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, based on the Tukey-Kramer procedure with an overall level of significance of 0.05, the retailer would decide that there is a significant difference between all pairs of mean speeds.

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, construct the ANOVA table from the sample data.

TABLE 10-19 An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields, 5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a completely randomized design, the results are presented in the table that follows. -Referring to Table 10-19, the null hypothesis should be rejected at 0.005 level of significance.

Which of the following components in an ANOVA table are not additive?