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i. In an independent-groups study, a Mediterranean diet is given to 50 people and a Paleo diet is given to 40 different people. Of interest is whether the Mediterranean diet lowers cholesterol levels more so than the Paleo diet. Participants in this study did not differ significantly at the start of the study with respect to their LDL, HDL, or total cholesterol levels, and were randomly assigned to the two treatment conditions. The Mediterranean group had a mean decrease of 12 mg/dl of LDL, with a standard deviation of 3 mg/dl. The Paleo diet group had a mean decrease in LDL of 8 mg/dl, with a standard deviation of 2 mg/dl.

a. For this between-groups study, state an appropriate set of hypotheses using the proper notation, where you are comparing two samples that are believed to be representative of the population. (2)

b. The result of this study yielded t = 1.496. Using the hypotheses you provided above, what conclusion can you make about the difference between these means at the p =.05 level of significance? Please indicate the critical value from the table, as well as the degrees of freedom associated with this study and statistical test. (3)