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, the value of the test statistic is
A) 8.532.
B) 15.483.
C) 18.889.
D) 69.744.

Question

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, the value of the test statistic is
A) 8.532. 
B) 15.483. 
C) 18.889. 
D) 69.744.

Quizplus · Accepted Answer

The test statistic for testing independence between two categorical variables (in this case, hours watching TV and weight category) is calculated as the chi-square statistic. From Table 12-13, we can see that the observed value of the test statistic is 18.889. To determine if this value is significant at the 1% level, we compare it to the critical value from the chi-square distribution with (number of rows - 1) x (number of columns - 1) degrees of freedom. In this case, the degrees of freedom is (3-1) x (3-1) = 4, and the critical value at the 1% level is 13.277. Since the observed value of the test statistic is greater than the critical value, we reject the null hypothesis of independence and conclude that there is a significant relationship between hours of TV watched and weight category in these children.

TABLE 12-13 Recent Studies Have Found That American Children Are More Obese