Question

A criminal justice researcher is interested in studying the relationship between the religious affiliation of offenders and sentence (in years) handed out. Here is the data she is working with:

Catholics	Protestants	Jews	Muslims
10	10	12	12
16	10	12	12
12	13	16	12
12	13	18	13
13	12	13	16
14	12	13	13
12	18	11	13
12	11	12	11
16	16	16	10
12	12	14	12

Calculate the within-group sum of squares. Calculate the between-group sum of squares. Calculate the mean square between groups (MSbetween). Calculate the mean square within groups (MSwithin). Calculate the F ratio.  Are your results statistically significant, and if so, at what level?  What are your conclusions about the null hypothesis?

Answer 1

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Catholics	10	129	12.9	3.655556
Protestants	10	127	12.7	6.455556
Jews	10	137	13.7	5.122222
Muslims	10	124	12.4	2.488889
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	9.275	3	3.091667	0.697806	0.559512	2.866266
Within Groups	159.5	36	4.430556
Total	168.775	39

Calculate the within-group sum of squares=159.5

Calculate the between-group sum of squares=9.275

Calculate the mean square between groups (MSbetween)=3.091667

Calculate the mean square within groups (MSwithin)= 4.430556

Calculate the F ratio= 0.697806

Are your results statistically significant, and if so, at what level?  

Since P value>alpha(0.05)

No the results are not significantly significance.

What are your conclusions about the null hypothesis?

Since P value>alpha(0.05). Reject the null hypothesis.

There is significant evidence that atleast one mean differs.