Greg would like to test whether he runs faster in the afternoon than in the morning, on average. In a sample of 10 morning runs, his average pace was 7 minutes 50 seconds per mile (470 seconds/mile), with a sample standard deviation of 45 seconds per mile. In a sample of 12 afternoon runs, his average pace was 7 minutes, 30 seconds per mile (450 seconds/mile), with a sample standard deviation of 32 seconds per mile. He assumes that running times are normally distributed in each population and that the population standard deviations are equal. Calling morning runs “population 1 "and afternoon runs “population 2”
a. Set up the null and alternative hypothesis.
b. What is the critical value at a 5% significance level?
c. What is the calculated test statistic?
d. Do you have evidence to reject the null hypothesis? What is your conclusion?