docx Page 1 of 25 1. Adult women's weights and adult men's weights are both normally distributed. A sample of five men and a sample of 15 women are randomly selected. The sample mean (X) and the population standard deviation (a) of these men and women are given below: Men Women n 5 15 X 196 39.59 146 33.31 2. By performing a test, would you be able to conclude that there are significant differences between men's and women's average weights, using a = 0.05. State your null and alternative hypotheses. (12+3 points) Assume that ACT scores are normally distributed. A sample of 25 male college freshmen and a sample of 16 female college freshmen are randomly selected. The sample mean (X) and the population standard deviation (a) of these male and female college freshmen are given below: n Female freshmen 16 Male freshmen 25 X 23.5 5.1 22.8 3.1 By performing a test, would you be able to conclude that the average ACT score for female freshmen is higher than that of the male freshmen, using a = 0.05? State your null and alternative hypotheses. (12+3 points) 3. Adult women's weights and adult men's weights are both normally distributed. Assume that a sample of five men and a sample of 15 women are randomly selected. The sample mean (X) and sample standard deviation (s) of these men and women are given below: n X S Men Women 5 196 15 146 39.59 33.31 By performing a test, would you be able to conclude that there are significant differences between men's and women's average weights, using a = 0.05. State your null and alternative hypotheses. Also perform a test to verify the assumption of equal variances. State your null and alternative hypotheses. (12+3+12+3 points) 4. A researcher is interested in assessing the impact of separation on friendship. She randomly selects 4 high school seniors about to be separated from their best friends by going to college. She asks them to rate their level of satisfaction with the friendship. After the first semester away from their best friends they rate their satisfaction again. Based on the data below, does separation have an impact of satisfaction with students' friendship? State your null and alternative hypotheses. Assume a=.05. (15+5 points) Participant Before After 1 40 32 2 38 31 13 36 30 4 42 31 5. A sample of 10 people was selected to participate in a new fitness program. Each participant's weight was measured before and after the program to see if the fitness program was effective in reducing their weights. The following are the recorded results: Before After 145 143 116 120 120 117 133 130 130 125 119 119 133 134 125 128 126 123 140 141 Perform a test to determine if the program is effective in weight loss. State your null and alternative hypotheses. Assume a = .05. (15+5 points)