Question: Data Set 8 in Appendix B includes a list of actual high temperatures and the corresponding list of three-day-forecast high temperatures. If the difference for each day is found by subtracting the three-day-forecast high temperature from the actual high temperature, the result is a list of 35 values with a mean of -1.3° and a standard deviation of 4.7°.

a. Construct a 99% confidence interval estimate of the mean difference between all actual high temperatures and three-day-forecast high temperatures.

b. Does the confidence interval include 0°? If a meteorologist claims that three-day-forecast high temperatures tend to be too high because the mean difference of the sample is 1.3°, does that claim appear to be valid? Why or why not?