Question

A researcher wishes to see whether there is any difference in the weight gains of athletes following one of three special diets. Athletes are randomly assigned to three groups and placed on the diet for six weeks. The weight gains (in pounds) are shown below. At α = 0.10, can the researcher conclude that there is a difference in the diets?

Diet A	Diet B	Diet C
3	10	8
7	12	3
6	11	2
4	14	5

a) What is the significance level?

b) State the null and alternative hypotheses.

c) What is the total sample size?

d) What is the degrees of freedom of the numerator?

e) What is the degrees of freedom of the denominator?

Answer 1

a ) Level of significance -----

b ) To test :

vs.

H1 : Atleast one inequality in H0 .

c ) Total sample size = 12

d ) Degrees of freedom of the numerator = 2

e ) Degrees of freedom of the denominator = 9

Test statistic :

We reject the null hypothesis or H0 if the

The ANOVA table is given below :

From the ANOVA table we can see , that ,

Hence we reject the null hypothesis or H0 .

Thus we have sufficient evidence to support the claim of the researcher that there is a difference in the diets .