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) Make a dotplot of the difference (High - Low) in temperature for each day.

(b) Historically, fall high and low temperatures on a given day differ by 30 F, on average. Describe what the graph reveals about whether temperatures differed more than usual this past fall.

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

(d) 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 30F, on average, this fall? Why or why not?