The data set actgpa contains the ACT composite scores and GPAs of some randomly selected seniors at a Midwest liberal arts college.
a) Give a 95% confidence interval for the mean ACT score of seniors at this school.
b) Give a 95% confidence interval for the mean GPA of seniors at this school.
c) What fraction of the variation in GPAs is explained by a student's ACT score?
d) Use the data to estimate with 95% confidence the average GPA for a student who scored 25 on the ACT.
e) Suppose you know a high school student who scored 30 on the ACT. Estimate with 95% confidence his GPA as a senior in college.
f) Are there any reasons to be concerned about the analyses you have just done? Explain.