Catherine Chao,Director of Marketing Research,is evaluating consumer acceptance of alternative toothpaste packages.She wonders whether acceptance is influenced by children in the household.Her staff prepared the following contingency table from a random sample of 100 households:
Using $\alpha$ = .05,the appropriate decision is ___.
A)reject the null hypothesis and conclude the two variables are not independent
B)do not reject the null hypothesis and conclude the two variables are not independent
C)reject the null hypothesis and conclude the two variables are independent
D)do not reject the null hypothesis and conclude the two variables are independent
E)do nothing

Question

Catherine Chao,Director of Marketing Research,is evaluating consumer acceptance of alternative toothpaste packages.She wonders whether acceptance is influenced by children in the household.Her staff prepared the following contingency table from a random sample of 100 households: 
 Using $\alpha$ = .05,the appropriate decision is ___.
A)reject the null hypothesis and conclude the two variables are not independent 
B)do not reject the null hypothesis and conclude the two variables are not independent 
C)reject the null hypothesis and conclude the two variables are independent 
D)do not reject the null hypothesis and conclude the two variables are independent 
E)do nothing

Quizplus · Accepted Answer

To determine whether the variables of toothpaste package acceptance and children in the household are independent, a chi-square test of independence can be performed. With a significance level of 0.05 and the given contingency table, the calculated chi-square value is 6.2925. The critical value at 1 degree of freedom is 3.841. As the calculated value exceeds the critical value, we reject the null hypothesis that the two variables are independent and conclude that they are not independent. Therefore, the appropriate decision is to reject the null hypothesis and conclude the two variables are not independent, which corresponds to choice letter A.

Catherine Chao,Director of Marketing Research,is Evaluating Consumer Acceptance of Alternative α\alphaα

Catherine Chao,Director of Marketing Research,is Evaluating Consumer Acceptance of Alternative $\alpha$