Exam 12: Chi-Square Tests and Nonparametric Tests

TABLE 12-6 According to an article in Marketing News, fewer checks are being written at the grocery store checkout than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below. -Referring to Table 12-6, there is sufficient evidence to conclude that the proportions between year 1 and year 2 are different at a 0.05 level of significance.

TABLE 12-6 According to an article in Marketing News, fewer checks are being written at the grocery store checkout than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below. -Referring to Table 12-6, what are the degrees of freedom of the test statistic?

TABLE 12-5 Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery, the operation is called a "clear" operation. A heart center wants to compare the proportion of clear operations for the 4 procedures and collects the following numbers of patients from their own records: They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05. -Referring to Table 12-5, the overall or mean proportion of clear operations is ________.

TABLE 12-3 The director of transportation of a large company is interested in the usage of her van pool. She considers her routes to be divided into local and non-local. She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes. She takes a sample of a day's riders and finds the following: She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05. -Referring to Table 12-3, the expected cell frequency in the Male/Local cell is ________.

TABLE 12-11 The director of admissions at a state college is interested in seeing if admissions status (admitted, waiting list, denied admission) at his college is independent of the type of community in which an applicant resides. He takes a sample of recent admissions decisions and forms the following table: He will use this table to do a chi-square test of independence with a level of significance of 0.01. -Referring to Table 12-11, the expected cell frequency for the Admitted/Urban cell is ________.

TABLE 12-1 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 12-1, what is the critical value when testing whether the population proportions are different if α = 0.10?

The McNemar test is approximately distributed as a Student's t.

TABLE 12-18 Two new different models of compact SUVs have just arrived at the market. You are interested in comparing the gas mileage performance of both models to see if they are the same. A partial computer output for twelve compact SUVs of model 1 and thirteen of model 2 is given below: You are told that the gas mileage population distributions for both models are not normally distributed. -Referring to Table 12-18, what is the p-value of the test statistic?

TABLE 12-11 The director of admissions at a state college is interested in seeing if admissions status (admitted, waiting list, denied admission) at his college is independent of the type of community in which an applicant resides. He takes a sample of recent admissions decisions and forms the following table: He will use this table to do a chi-square test of independence with a level of significance of 0.01. -Referring to Table 12-11, the p-value of this test is greater than 0.01.

TABLE 12-18 Two new different models of compact SUVs have just arrived at the market. You are interested in comparing the gas mileage performance of both models to see if they are the same. A partial computer output for twelve compact SUVs of model 1 and thirteen of model 2 is given below: You are told that the gas mileage population distributions for both models are not normally distributed. -Referring to Table 12-18, what is your decision on the test using a 5% level of significance?

TABLE 12-16 A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12 fluid ounces and a standard deviation of 0.5 ounces. The company wants to test whether the standard deviation of the amount filled by the machine is 0.5 ounces. A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces. -Referring to Table 12-16, which is the appropriate test to use?

TABLE 12-12 Parents complain that children read too few storybooks and watch too much television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks. -Referring to Table 12-12, if the null hypothesis of no connection between time spent watching TV and time spent reading storybooks is true, how many children watching less than 2 hours of TV and reading more than 2 hours of storybooks on average can we expect?

TABLE 12-5 Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery, the operation is called a "clear" operation. A heart center wants to compare the proportion of clear operations for the 4 procedures and collects the following numbers of patients from their own records: They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05. -Referring to Table 12-5, the critical value of the test is ________.

TABLE 12-7 Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below. At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities. -Referring to Table 12-7, there is sufficient evidence to conclude that the proportions between New York and Paris are different at a 0.05 level of significance.

TABLE 12-2 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 12-2, the hypotheses the dean should use are

TABLE 12-12 Parents complain that children read too few storybooks and watch too much television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks. -Referring to Table 12-12, to test whether there is any relationship between average time spent watching TV and average time spent reading storybooks, the value of the measured test statistic is

TABLE 12-18 Two new different models of compact SUVs have just arrived at the market. You are interested in comparing the gas mileage performance of both models to see if they are the same. A partial computer output for twelve compact SUVs of model 1 and thirteen of model 2 is given below: You are told that the gas mileage population distributions for both models are not normally distributed. -Referring to Table 12-18, what is your conclusion on the test using a 5% level of significance?

TABLE 12-13 Recent studies have found that American children are more obese than in the past. The amount of time children spent watching television has received much of the blame. A survey of 100 ten-year-olds revealed the following with regards to weights and average number of hours a day spent watching television. We are interested in testing whether the mean number of hours spent watching TV and weights are independent at 1% level of significance. -Referring to Table 12-13, which of the following statements is correct?

TABLE 12-17 A perfume manufacturer is trying to choose between 2 magazine advertising layouts. An expensive layout would include a small package of the perfume. A cheaper layout would include a "scratch-and-sniff" sample of the product. The manufacturer would use the more expensive layout only if there is evidence that it would lead to a higher approval rate. The manufacturer presents the more expensive layout to 4 groups and determines the approval rating for each group. He presents the "scratch-and-sniff" layout to 5 groups and again determines the approval rating of the perfume for each group. The data are given below. Use this to test the appropriate hypotheses with the Wilcoxon rank sum test with a level of significance of 0.05. -Referring to Table 12-17, the null hypothesis should be rejected.

In testing a hypothesis using the X² test, the theoretical frequencies are based on the