We are interested in examining whether a diet with a high amount of rapidly absorbed carbohydrates increases

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Question:

We are interested in examining whether a diet with a high amount of rapidly absorbed carbohydrates increases risk of type 2 diabetes. We have data on 40 subjects who have been consuming a low glycemic load diet for 1 year and another 40 subjects who have been consuming a high glycemic index diet for 1 year. By the end of the year, 7 of the subjects consuming the high GI diet developed insulin resistance, while 4 subjects in the low GI group developed insulin resistance.

A) Using the normal theory method, test if there is a significant difference between these groups. Use a two sided test with an alpha of .05 and assume that the normal approximation to the binomial distribution is valid.

B) Find the exact p-value for #A.

C) Using the contingency table method, test if there is a significant difference between these groups. Use a two sided test with an alpha of .05.

D) Estimate the p-value for #C.