a. In year 2017, the mean and standard deviation for the quality grade point average of the first year students in a basic statistics course are found to be 2.95 and 0.53. If 38 undergraduates are randomly selected, find the 95% confidence interval for the mean of the entire group.

b. Within the same year, if another group of 38 students were sampled and resulted with a mean of 2.87, test the hypothesis that the sample mean is different from the population mean at 5% level of significance.