You were recently accepted to the college of your choice. On your first day, you are walking to your next class when you notice a bill on the Mathematics Department's billboard. Apparently the department offers a $50 cash prize to anyone who can solve their weekly math puzzle and turn in their answer to the department's secretary. The prize is limited to non-Math majors or minors only, and since you are still undeclared you decide to give it a chance. This weeks math puzzle is:

Arecent 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. statistic men women sample mean 24.85 21.33 sample standard deviation 5.54 4.93 sample size 34 36 at the 0.01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month? state the decision rule for 0.01 significance level: h0: μmen= μwomen h1: μmen ≠ μwomen. (negative amounts should be indicated by a minus sign. round your answers to 3 decimal places.) compute the value of the test statistic. (round your answer to 3 decimal places.) what is your decision regarding the null hypothesis? what is the p-value? (round your answer to 3 decimal places.)