A class survey in a large class for first year college students asked “About how many minutes do you study on a typical weeknight?” The mean response of the 269 students was Xbar = 137 minutes. Suppose that we know that the study time follows a Normal distribution with standard deviation σ = 65 minutes in the population of all first year students at this university.
a) Use the survey result to give a 99% confidence interval for the mean study time of all first year students.
b) What condition not yet mentioned is needed for your confidence interval to be valid? (It is suggested that SPSS be used to solve this problem)
Solution: (a) We know the population standard deviation, so the confidence interval is computed using the following formula:
(b) We need the sample to be a random sample. The approximate normality is guaranteed by the Central Limit theorem, given the large sample size (n = 269)