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 observed value of chi-square is ______________.

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 observed value of chi-square is ______________.

Quizplus · Accepted Answer

A chi-square test for independence is appropriate to test whether there is a relationship between toothpaste package preference and the presence of children in the household. Using the contingency table provided, we calculate the expected frequencies and then the chi-square test statistic. With a sample size of 100 and 2 degrees of freedom (1 for rows and 1 for columns), the critical value of chi-square at alpha = .05 is 5.99. The observed value of chi-square is 13.19, which is greater than the critical value. Therefore, we reject the null hypothesis that toothpaste package preference is independent of the presence of children in the household.

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 $\alpha$