Several clinical researchers investigated the most effective

Several clinical researchers investigated the most effective nutritional plans for reducing LDL cholesterol. They selected 3 diets: (1) a saturated-fat diet; (2) the Mediterranean diet:; and (3) the U.S. National Cholesterol Education Program NCEP-1) Diet. Before the experiment was conducted, the patients studies were shown to initially have the same LDL levels, and they were randomly assigned to 1 of the 3 nutritional treatment groups. The results are listed in the table below.

Saturated Fat Diet                                       Mediterranean Diet                                             NCEP-1 Diet

        245                                                                         56                                                                           125

        123                                                                         78                                                                           100

        166                                                                         101                                                                         140

        104                                                                         158                                                                         151

        196                                                                         145                                                                         138

Q(8) State the null and alternative hypotheses.

Q(9) Which test is best employed here? Explain your reasoning.  

Q(10) What test statistic(s) should be utilized here? Explain your reasoning.  

Q(11) Test the claim that the mean LDL cholesterol levels are different at the 95% significance levels.

Q(12) Draw boxplots of the 3 LDL cholesterol levels for the 3 groups to support the above results.  

Solution

Sol)

8) H0: All the treatment group means are equal

H1: All the treatment group means are not equal

9)

Here we need to test the homogenity of three means we use ANOVA one way( F test).

10)

F statistic =MSt / MSE

11)

From excel

F cal=3.8852

and P value =0.129059

P > alpha(0.05) we accept the null hypothesis.