She had 8 times recorded when she ran in the morning and these had a sample average of 132.52 minutes with a Standard deviation of 1.31 minutes. In addition, she had 10 times recorded when she ran in the afternoon and these had a sample average of 133.87 minutes with a standard deviation of 1.72 minutes.
(a) Is there sufficient evidence to conclude that the morning and afternoon are any different on average? Use an appropriate hypothesis test to investigate this question.
(b) Construct a two-sided 99% confidence interval for the difference between the average run time in the morning and the average run time in the afternoon.