Problem 3Your professor wants to identify the average GPA of the undergraduate students in his department. He selects a random sample of 16 students and finds that the average GPA in this sample is 3.33 with a sample standard deviation of 0.33. Assume that the GPA scores are normally distributed but the population variance is unknown.(a) Construct an interval estimate for the average GPA of the FRED undergraduate students with a 0.95 level of confidence.(b) Construct an interval estimate for the average GPA of the FRED undergraduate students with a 0.80 level of confidence.(c) Compare the two interval estimates. Are they different? If yes explain why and discuss how a lower/higher confidence level affects the width of the interval estimate and the probability that the interval will contain the true population parameter of interest (in this case the average GPA of the FRED undergraduates).
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