Question 7: An experiment was conducted to see if exercise helps lose weight. Fives volunteers were weighed before and after doing exercises. Their weights (in pounds) are Person 1 2 3 4 5 Before 168 180 220 150 171 After 160 173 209 151 170 Assume that weight of the volunteers before and after exercises follows normal distributions with mean #1 and \"2 respectively. 1. Perform a hypothesis test for this experiment at the 5% signicant level. (3pts) 2. Construct a 90% condence interval for H1 p2 (3pts) Question 8: We want to test if the average weight of women is different from the average weight of men. Assume that the average weight of women and of men follow normal distributions with mean #1 and M2 respectively. To perform the test, we collect data from 12 women and 10 men. For women, the sample mean is 70 and the sample standard deviation is 20. For men, the sample mean is 80 and the sample standard deviation is 30. 1. Perform a hypothesis test at the 5% signicant level. (3pts) 2. What type of error might we have committed? (1pt) 3. Construct a 90% condence interval for H1 M2 (3pts)