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,

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 10-19 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 test is valid only if the population of crop yields is normally distributed for the three varieties.

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 value of the test statistic is ________.

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, 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 ________.

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 the three means other than the mean for Tornado are not significantly different from each other.

In testing for the differences between the means of two independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are

F tests are one-tail tests.

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, what is(are)the critical value(s)of the relevant hypothesis test if the level of significance is 0.01?

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?

TABLE 10-9 The following Microsoft Excel output contains the results of a test to determine whether the proportions of satisfied customers at two resorts are the same or different. -Referring to Table 10-9, construct a 90% confidence interval estimate of the difference in the population proportion of satisfied customers between the two resorts.

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, 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 correct?

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 10-19 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 Walsh and Trevor seeds.

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, the p-value of the test statistic 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, what is a point estimate for the mean of the sampling distribution of the difference between the two sample means?

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, you must assume that the population of difference scores is normally distributed.

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 value of the test statistic for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels?

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 related samples.

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, using an overall level of significance of 0.01, the critical value of the Studentized range Q used in calculating the critical range for the Tukey-Kramer procedure is ________.