A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of 42 pounds with a standard deviation of 12 pounds. The liquid diet group had a mean weight loss of 45 pounds with a standard deviation of 14 pounds. Conduct a hypothesis test at the 5% level. NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) + Part (a) + Part (b) [+ Part (c) Part (d) State the distribution to use for the test. (Enter your answer in the form z or towhere of is the degrees of freedom. Round your answer to two decimal places.) T 48 X Part (e) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.) t = -1.036 X Part (f) What is the p-value? (Round your answer to four decimal places.)