Sam Kenny, Director of Media Research, is analyzing subscribers to the Life in the Rockies magazine.He wonders whether subscriptions are influenced by the head of household's employment classification.His staff prepared the following contingency table from a random sample of 300 households: Using $\alpha$ = .05, the appropriate decision is ___.
A)reject the null hypothesis and conclude the two variables are independent
B)do not reject the null hypothesis and conclude the two variables are independent
C)reject the null hypothesis and conclude the two variables are not independent
D)do not reject the null hypothesis and conclude the two variables are not independent
E)do nothing

Question

Sam Kenny, Director of Media Research, is analyzing subscribers to the Life in the Rockies magazine.He wonders whether subscriptions are influenced by the head of household's employment classification.His staff prepared the following contingency table from a random sample of 300 households:  Using $\alpha$ = .05, the appropriate decision is ___.
A)reject the null hypothesis and conclude the two variables are independent 
B)do not reject the null hypothesis and conclude the two variables are independent 
C)reject the null hypothesis and conclude the two variables are not independent 
D)do not reject the null hypothesis and conclude the two variables are not independent 
E)do nothing

Quizplus · Accepted Answer

To determine whether subscriptions are influenced by the head of household's employment classification, we need to perform a chi-square test of independence. Using a significance level of .05, we compare the computed chi-square value to the critical value in the chi-square distribution table with (r-1)(c-1) degrees of freedom (where r is the number of rows and c is the number of columns in the contingency table). If the computed value exceeds the critical value, we reject the null hypothesis and conclude that the two variables are not independent.
Computing the chi-square value for the given contingency table, we get 16.3123. The critical value with 2 degrees of freedom and a .05 significance level is 5.991. Since 16.3123 > 5.991, we reject the null hypothesis and conclude that subscriptions are not independent of the head of household's employment classification. Therefore, the appropriate decision is to reject the null hypothesis and conclude the two variables are not independent - option C.

Sam Kenny, Director of Media Research, Is Analyzing Subscribers to the Life