Question

1. Suppose we wanted to compare the somatic complaints (as measured on a scale known as the Physical Symptom Survey or PSS) of three groups of people: nonsmokers, smokers, and people who recently quit smoking. Using the following data for PSS scores, do a one-way ANOVA to test the hypothesis that the population means are equal:

Nonsmokers	Smokers	Quitters
19	26	37
23	29	32
17	22	27
20	30	41
26	23	38

What are the means for the three groups? Compute the sums of squares, degrees of freedom, and mean squares for these data. What is value of F? Using an alpha of .05, is the F statistically significant? Describe the results of the analyze.

Answer 1

The following table is obtained:

	Group 1	Group 2	Group 3
	19	26	37
	23	29	32
	17	22	27
	20	30	41
	26	23	38
Sum =	105	130	175
mean =	21	26	35
∑i​Xij2​=	2255	3430	6247
St. Dev. =	3.536	3.536	5.523
SS =	50	50	122
n =	5	5	5

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that  F is statistically significant at the \alpha = 0.05α=0.05 significance level

Finally we get the Anova table as

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	503.3333	2	251.6667	13.6036	0.000822	3.885294
Within Groups	222	12	18.5
Total	725.3333	14