Question

A recent study found that 62 children who watched a commercial for potato chips featuring a celebrity endorser ate a mean of 37 grams of potato chips as compared to a mean of 27 grams for 52 children who watched a commercial for an alternative food snack. Suppose that the sample standard deviation for the children who watched the​ celebrity-endorsed commercial was 21.1 grams and the sample standard deviation for the children who watched the alternative food snack commercial was 12.9 grams.

A. Assuming that the population variances are equal and α=0.05​, is there evidence that the mean amount of potato chips eaten was significantly higher for the children who watched the​ celebrity-endorsed commercial? Let population 1 be the weights of potato chips eaten by children who watched the​ celebrity-endorsed commercial and let population 2 be the weights of potato chips eaten by children who watched the alternative food snack commercial. What are the correct null and alternative​ hypotheses?

What is the test​ statistic?

What is the corresponding​ p-value? What is the correct​ conclusion?

B. Assuming that the population variances are​ equal, construct a 95​% confidence interval estimate of the difference μ1−μ2 between the mean amount of potato chips eaten by the children who watched the​ celebrity-endorsed commercial and children who watched the alternative food snack commercial.

C. Compare and discuss the results of​ (a) and​ (b).

Answer 1