Eight people with high blood cholesterol have changed their diets to avoid foods high in cholesterol, such as meats and dairy products. After two months on this diet, their cholesterol levels are...

Eight people with high blood cholesterol have changed their diets to avoid foods high in cholesterol, such as meats and dairy products. After two months on this diet, their cholesterol levels are re-measured.  The following data are changes in their cholesterol levels in mg/dL (=final measure –initial measure):

-40             -27                  14                    -8        -31          10         -38           -26

a. Test the hypothesis that consuming a low cholesterol diet for two months affects blood cholesterol levels. (Hint: if there is a difference, then the change won’t be equal to zero.) Follow the 4 steps of hypothesis testing, stating your null and alternative hypothesis in symbols, and giving a complete finding in plain English with detailed statistical notation.

b. Now test the hypothesis that consuming a low cholesterol diet for two months decreases blood cholesterol levels by 10 mg/dL. Again, show all 4 steps. (Hint: remember that a null hypothesis of “no difference” can be “not different from a particular value.”)