A high school counselor wanted to know if tenth-graders at her high school tend to have more free time than the twelfth-graders. She took random samples of 25 tenth-graders and 23 twelfth-graders. Each student was asked to record the amount of free time he or she had in a typical week. The mean for the tenth graders was found to be 29 hours of free time per week with a standard deviation of 7.0 hours. For the twelfth graders, the mean was 22 hours of free time per week with a standard deviation of 6.2 hours. Assume that the two populations are normally distributed with equal but unknown population standard deviations.
a. Make a 90% confidence interval for the difference between the corresponding population means.
b. Test at a 5% significance level whether the two population means are different.