Atravel magazine conducts an annual survey where readers rate their favorite cruise ship. ships are rated on a 10 point scale, with higher values indicating better service. a sample of 50 ships that carry fewer than 500 passengers resulted in a average rating of 6.89 with standard deviation 0.52. a sample of 55 ships that carry more than 500 passengers resulted in an average rating of 6.55 with standard deviation 0.83. give a 99.8% confidence interval of the difference between the population mean ratings for smaller ships and the population mean ratings for larger ships. (note, the order of subtraction at the wording carefully.)

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.)