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

-Referring to Table 12-11, suppose we want to constrain the probability of committing a Type I error to 5% when testing whether there is any relationship between average time spent watching TV and average time spent reading story books, the critical value will be
A) 5.991.
B) 7.378.
C) 12.592.
D) 14.449.

Question

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
 
-Referring to Table 12-11, suppose we want to constrain the probability of committing a Type I error to 5% when testing whether there is any relationship between average time spent watching TV and average time spent reading story books, the critical value will be
A) 5.991. 
B) 7.378. 
C) 12.592. 
D) 14.449.

Quizplus · Accepted Answer

To test whether there is any relationship between average time spent watching TV and average time spent reading storybooks, we need to conduct a hypothesis test. If we want to constrain the probability of committing a Type I error to 5%, we need to choose a significance level of 0.05. Since we have a large sample size of 1,000, we can use a z-test for the difference between two population means. The critical value for a two-tailed z-test with a significance level of 0.05 is 1.96. However, we are interested in testing for any relationship (positive, negative or no relationship) between the two variables, so we need to use a two-tailed test. The critical value for a two-tailed z-test with a significance level of 0.05 is therefore 1.96 x 2 = 3.92. However, the options given are all greater than 3.92. These are critical values for a chi-square test with 1 degree of freedom, which is not appropriate for this scenario. The correct critical value for a two-sample z-test with a two-tailed alternative hypothesis and a significance level of 0.05 is 1.96 x 2 = 3.92. However, this value is not one of the options provided. Of the options given, the closest value to 3.92 is 5.991, which corresponds to a chi-square test with 1 degree of freedom and a significance level of 0.05.

TABLE 12-11 Parents Complain That Children Read Too Few Storybooks and Watch