Exam 12: Chi-Square Tests and Nonparametric Tests

If the assumptions of the one-way ANOVA F test are not met, which of the following tests could be used?

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: Data Level of Significance Population 1 Sample Sample Size 12 Sum of Ranks 192.5 Population 2 Sample Sample Size 13 Sum of Ranks 132.5 Intermediate Calculations Total Sample Size n 25 You are told that the gas mileage population distributions for both models are not normally distributed. -Referring to Table 12-18, what is the standard deviation of the Wilcoxon rank sum test statistic T₁?

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. Average time spent reading story books Average time spent watching TV Less than 1 hour Between land 2 hours More than 2 hours Less than 2 hours 90 85 130 More than 2 hours 655 32 8 -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: Data Level of Significance Population 1 Sample Sample Size 12 Sum of Ranks 192.5 Population 2 Sample Sample Size 13 Sum of Ranks 132.5 Intermediate Calculations Total Sample Size n 25 You are told that the gas mileage population distributions for both models are not normally distributed. -Referring to Table 12-18, what is the value of the Z test statistic?

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. Year Check Written Year 1 Year 2 Year 3 Yes 225 175 125 No 275 325 375 -Referring to Table 12-6, what is the value of the test statistic?

TABLE 12-10 One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. Since the job is repetitious, after the initial training period any improvement due to a learning effect might be offset by a loss of motivation. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table below. Years Since Training Period Digefect Rate: High <1 Year 1-4 Years 5-9 Years 6 9 9 Average 9 19 23 Low 7 8 10 -Referring to Table 12-10, what is the expected number of employees with 1 to 4 years of training time and a high defect rate?

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. 52 37 68 43 43 53 48 39 47 -Referring to Table 12-17, the hypotheses that should be used are

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. TV Hours Weights 0-3 3-6 6+ Total More than 10 lbs. overweight 1 9 20 30 Within 10 lbs. of normal weight 20 15 15 50 More than 10 lbs. underweight 10 5 5 20 Total 31 29 40 100 -Referring to Table 12-13, the test is always a one-tail test.

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: Admitted Wait List Denied Total Urban 45 21 17 83 Rural 33 13 24 70 Suburban 34 12 39 85 Total 112 46 80 238 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 alternative hypothesis claims that "there is some connection between admission status at the college and the type of community in which an applicant resides."

The Kruskal-Wallis test is an extension of which of the following for two independent samples?

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, what is the value of the test statistic?

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. Year Check Written Year 1 Year 2 Year 3 Yes 225 175 125 No 275 325 375 -Referring to Table 12-6, what is the expected number of shoppers who do not pay by check in year 3 if there is no difference in the proportion of shoppers who pay by check among the three years?

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. Hong Kong New York Paris Yes 86\% 76\% 78\% No 14\% 24\% 22\% 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, the expected cell frequency for the Paris/No cell 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. Hong Kong New York Paris Yes 86\% 76\% 78\% No 14\% 24\% 22\% 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, what are the values of the absolute difference and the critical range for the Marascuilo procedure to test for the difference in proportions between Hong Kong and New York using a 0.05 level of significance?

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: Admitted Wait List Denied Total Urban 45 21 17 83 Rural 33 13 24 70 Suburban 34 12 39 85 Total 112 46 80 238 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 same decision would be made with this test if the level of significance had been 0.005.

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, what type of test should be performed?

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 p-value of the test 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: Data Level of Significance Population 1 Sample Sample Size 12 Sum of Ranks 192.5 Population 2 Sample Sample Size 13 Sum of Ranks 132.5 Intermediate Calculations Total Sample Size n 25 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 12-2 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 null hypothesis will be rejected if the test statistic is ________.

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: Procedure A B C D Total Clear 27 41 21 7 96 Return 11 15 9 11 46 Total 38 56 30 18 142 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, there is sufficient evidence to conclude that the proportions between procedure A and procedure B are different at a 0.05 level of significance.