Students at Rolling Rock University claim that their school is superior to vaunted Bigbrain University with regard to achievement on a national aptitude test, where the mean is 500 and the standard deviation is 100. A random sample of students is obtained from each university, the mean for the Rolling Rock sample is found to be higher than the mean for the Bigbrain sample, and the 95% confidence interval for the difference between two means is computed. What should the Rolling Rock students conclude if this confidence interval is:

(a) −7.63 to 13.44?

(b) 2.27 to 19.85?

(c) 97.22 to 122.44?

(d) Compare examples (b) and (c). How does this comparison illustrate the advantages that confidence intervals have over testing a specific null hypothesis, such as whether the difference between the means of Rolling Rock University and Bigbrain University is zero?