Richard is designing a new website for students to create study groups and collaborate with other students.
the site will launch with five study groups, each with its creator as its only member, and richard anticipates that two study groups will be added every month. he also estimates that seven new members will be added to each study group every month.
the estimate for the total number of group members is given by the polynomial expression below, where x is the number of months since the site's launch.

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.)