Exam 12: Chi-Square Tests and Nonparametric Tests

TABLE 12-12 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 average 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 12-12, what is the value of the test statistic?

TABLE 12-12 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 average 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 12-12, the degrees of freedom of the test statistic are

TABLE 12-6 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 12-6, the null hypothesis will be rejected if the test statistic is _____ .

The McNemar test is approximately distributed as a standardized normal random variable.

TABLE 12-11 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. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\text { Average time spent reading story books }$ Average time spent watching TV Less than 1 hour Between 1 and 2 hours More than 2 hours Less than 2 hours 90 85 130 More than 2 hours 655 32 8 -Referring to Table 12-11, how many children in the survey spent less than 2 hours watching TV and more than 2 hours reading story books on average?

TABLE 12-9 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 12-18, the decision rule for a level of significance of 0.05 using the Kruskal-Wallis test is to reject the null hypothesis if the test statistic H is _______assuming that the sample sizes are large enough to use a chi-square approximation.