Question

A recent study found that 65 children who watched a commercial for potato chips featuring a celebrity endorser ate a mean of 36 grams of potato chips as compared to a mean of 25 grams for 55 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 21.5 grams and the sample standard deviation for the children who watched the alternative food snack commercial was 12.6 grams

a. Assuming that the population variances are equal and a = 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?

Answer 1

The correct null and alternative hypotheses for the study on potato chips consumption induced by a celebrity-endorsed commercial are H0: μ1 - μ2 = 0 and Ha: μ1 - μ2 > 0, respectively. A two-sample t-test assuming equal population variances at an alpha level of 0.05 can be used to test these hypotheses.

Step-by-step explanation:

To determine whether there is evidence that the mean amount of potato chips eaten was significantly higher for the children who watched the celebrity-endorsed commercial, we conduct a two-sample t-test for means. The null hypothesis (H0) for this study is that there is no difference in the mean amount of potato chips eaten by the two groups of children; mathematically, this can be stated as H0: μ1 - μ2 = 0, where μ1 is the mean for the celebrity-endorsed commercial group and μ2 is the mean for the alternative food snack commercial group. The alternative hypothesis (Ha) posits that there is a difference, specifically that the mean for the celebrity-endorsed commercial group is higher; this is expressed as Ha: μ1 - μ2 > 0.

Because we assume equal population variances and have an alpha level (α) of 0.05, the t-test will tell us if we can reject the null hypothesis in favor of the alternative hypothesis. The test is directional (one-tailed) as we are only interested in whether the mean amount for the celebrity-endorsed group is greater, not if it is just different.