This past fall, temperatures in a particular city seemed to fluctuate tremendously. The days often felt like summer and the nights often felt like winter. A weather analyst selected a simple random sample of 9 days from this past fall and recorded the high and low temperature in this city for each of the days.

Day 1 2 3 4 5 6 7 8 9

High Temp F 78 85 72 82 78 77 80 78 82

Low Temp F 42 50 44 48 48 45 45 41 47

(a). Calculate the mean difference in temperature and the standard deviation of the differences. Interpret the mean difference.

(b). A 99% confidence interval for the true mean difference (High - Low) in daily temperature is (30.242, 36.869). Based on this interval, can you conclude that the daily temperature differed by more than 30*F, on average, this fall? Why or why not?