In the following table, likely voters' preferences of two candidates are cross-classified by gender. Using the p-value approach and α = 0.10, the decision and conclusion are ________.
A) reject the null hypothesis; gender and candidate preference are dependent
B) do not reject the null hypothesis; gender and candidate preference are independent
C) reject the null hypothesis; gender and candidate preference are independent
D) do not reject null hypothesis; gender and candidate preference are dependent

Question

In the following table, likely voters' preferences of two candidates are cross-classified by gender.  Using the p-value approach and α = 0.10, the decision and conclusion are ________.
A) reject the null hypothesis; gender and candidate preference are dependent 
B) do not reject the null hypothesis; gender and candidate preference are independent 
C) reject the null hypothesis; gender and candidate preference are independent 
D) do not reject null hypothesis; gender and candidate preference are dependent

Quizplus · Accepted Answer

Using the p-value approach with alpha=0.10, we compare the calculated p-value to the alpha level. If p-value is less than or equal to alpha, we reject the null hypothesis. Here, the p-value is not given in the table, but we can use a chi-square test to calculate it. The chi-square test statistic is 8.55 with 1 degree of freedom. Looking up the p-value in a chi-square distribution table with 1 degree of freedom gives a p-value of 0.0034. Since 0.0034 is less than 0.10, we reject the null hypothesis. Therefore, we conclude that gender and candidate preference are dependent.

In the Following Table, Likely Voters' Preferences of Two Candidates