Please answer with solution:

**Tests Concerning the difference between population means**

1. To test the effect of a physical fitness course on one's physical ability, the number of sit-ups that a person could do in one minute, both before and after the course, was recorded. Ten randomly selected participants scores as shown in the following table. Can you conclude that a significant amount of improvement took place? Use a 0.01 level of significance.

Before 29, 22, 25, 29, 26, 24, 31, 46, 34, 28

After 39, 26, 25, 35, 33, 36, 32, 54, 50, 43

**Test Concerning Proportions**

1. Twenty one out of 100 randomly selected women said they use seat belts, while 117 out of 180 men said the same. Test the claim that men are more safety conscious than women based one the use of seat belts at a 0.01 level of significance. Construct a 99% confidence interval to test the claim.

2. Labor statistics indicate that 88 out of 100 cashiers and servers are women. A random sample of cashiers and servers in a large city indicate that 124 of 150 cashiers and 200 of 250 servers are women. Is there a significant difference in the proportion of servers and proportion of cashiers who are women at 0.05 level of significance?