Question

The data below represents the weight loss (in pounds) for people on three different exercise programs. At the 0.01 significance level, does it appear that a difference exists in the true mean weight loss produced by the three exercise programs.

Exercise A	Exercise B	Exercise C
7.1	3.1	6.7
8.0	2.2	8.1
7.5	5.0	5.0
6.8	4.4	9.0

a) State the null and alternative hypotheses.

b) Find the P-value. STATE THE CALCULATOR COMMAND YOU USE.

c) State whether you should reject or fail to reject the null hypothesis. Justify your answer.

d) State your conclusion in non-technical terms. Which exercise program appears to be the least effective based on the sample data?

Answer 1

	Mean	n	Std. Dev
Exercise A	7.35	4	0.520
Exercise B	3.68	4	1.263
Exercise C	7.20	4	1.745
Total	6.08	12	2.118

Part a)

To Test :-
H0 :- µ1 = µ2 = µ3 = 0 i.e There is no difference in the treatment means
H0 :- µ1 = µ2 = µ3 ≠ 0 i.e Some means are different

Part b)

ANOVA table
Source	SS	df	MS	F	p-value
Treatment	34.605	2	17.3025	10.57	0.0043
Error	14.738	9	1.6375
Total	49.343	11

Excel formula

FDIST(10.5664,2,9) = 0.004349242

Part c)

Decision based on P value
Reject null hypothesis if P value < α = 0.01
Since P value = 0.0043 < 0.01, hence we reject the null hypothesis
Conclusion :- Treatment means differs

Part d)

There is sufficient evidence to conclude that a difference exists in the true mean weight loss produced by the three exercise programs.

Lookinat at the averages we can say that Exercise B is lease effective.