In a completely randomized experimental design 11 experiment

In a completely randomized experimental design, 11 experimental units were used for each of the 3 treatments. Part of the ANOVA table is shown below.

            Source of            Sum                Degrees         Mean

            Variation        of Squares       of Freedom     Squares                F

            Between

            Treatments          1,500                        ?                     ?                      ?

            Within

            Treatments                   ?                      ?                     ?

            (Error)

            Total                   6,000

            a.   Fill in the blanks in the above ANOVA table.

            b.   At 95% confidence, test to determine whether or not the means of the 3 populations are equal.

Solution

a.

b. Looking up on the F table with numerator degrees of freedom=2 and denominator degrees of freedom=8 yields a critical value of 4.46. Since our calculated F ratio of 1.33 is not more extreme than this value, we would not reject the null hypothesis. There is not sufficient evidence to say that any of the treatment means are different.