(Solved): A recent study focused on the number of times men and women who live alone buy take-out dinner in ...

A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. Assume that the distributions follow the normal probability distribution and the population standard deviations are equal. The information is summarized below. At the .01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month? Required: a. State the null and alternate hypotheses. \[ \begin{array}{l} H_{0}: \mu_{\text {Men }}=\mu_{\text {Women }} H_{1}: \mu_{\text {Men }} \neq \mu_{\text {Women }} \\ H_{0}: \mu_{\text {Men }} \neq \mu_{\text {Women }} H_{1}: \mu_{\text {Men }}=\mu_{\text {Women }} \\ H_{0}: \mu_{\text {Men }} \neq \mu_{\text {Women }} H_{1}: \mu_{\text {Men }} \neq \mu_{\text {Women }} \end{array} \] b. Compute the test statistic. (Round your answer to 3 decimal places.) c. Compute the p-value. NOTE: P-value calculators are available through online search. (Round your answer to 4 decimal places.)