Solve both questions hand written and show work

5. Independent random samples from normal populations produced the results shown below. Assume the variance of the two samples are the same. Sample 1: 5.8, 5.1, 3.9, 4.5, 5.4 Sample 2: 4.4, 6.1, 5.2, 5.7 (1) Can we conclude that uj is less than /2 by more than 1 using a = .10. (15 points) (2) Use P-value method to perform above hypothesis at a = .20 (5 points) (3) Find a 95% confidence interval for (#1 - 12) for a two-sided interval. (5 points) A new weight-reducing technique, consisting of a liquid protein diet, is currently undergoing tests by the Food and Drug Administration (FDA) before its introduction into the market. The weights of a random sample of five people are recorded before they are introduced to the liquid protein diet. The five individuals are then instructed to follow the liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds) are again recorded. The results are listed in the table. Person Weight Before Diet Weight After Diet 167 160 212 207 13 205 202 214 208 221 217 (1) Is there a significant difference between the means of the weights before and after the diet? Use a = 0.05 (4 points)