A recent study ("Snack Ads Spur Children to Eat More," The NewYork Times, July 20, 2009, p. B3) found that children who watched a cartoon with food advertising ate, on average, 28.5 grams of Goldfish crackers as compared to an average of 19.7 grams of Goldfish crackers for children who watched a cartoon without food advertising. Although there were 118 children in the study, neither the sample size in each group nor the sample standard deviations were reported. Suppose that there were 59 children in each group, and the sample standard deviation for those children who watched the food ad was 8.6 grams and the sample standard deviation for those children who did not watch the food ad was 7.9 grams.
a. Assuming that the population variances are equal and α = 0.05, is there evidence that the mean amount of Goldfish crackers eaten was significantly higher for the children who watched food ads?
b. Assuming that the population variances are equal, construct a 95% confidence interval estimate of the difference between the mean amount of Goldfish crackers eaten by the children who watched and did not watch the food ad.
c. Compare the results of (a) and (b) and discuss.