Suppose we randomly contact $300$ married women and $200$ married men, who all own dogs. One hundred of the women and $36$ of the men replied that their pets are better listeners than their spouses. Organize this information into a contingency table. At the $0\mathrm{.}05$ significance level, is there a difference between the responses of women and men?

Required:

a$.$ Select the null hypothesis and the alternate hypothesis.

Select the null hypothesis and the alternate hypothesis.

$H_0-$ Listening and gender are not related and $H_1.$ Listening and gender are related.

b$.$ State the decision rule, using the $0\mathrm{.}05$ significance level. Note: Round your answer to $3$ decimal places.

Reject $H_0$ if chi$-$square $>$

c$.$ Compute the value of chi$-$square.

Note: Round your answer to $3$ decimal places.

Chi$-$square