Question

Random samples of employees from three different departments of MNM Corporation showed the following yearly incomes (in $1,000).

Department A	Department B	Department C
40	46	46
37	41	40
43	43	41
41	33	48
35	41	39
38	42	44

     Anova: Single factor

SUMMARY
Groups	Count	Sum	Average	Variance
Department A	6	234	39	8.4
Department B	6	246	41	18.8
Department C	6	258	43	12.8
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	48	2	24	1.8	0.20	3.68
Within Groups	200	15	13.33
Total	248	17

a.State the null and alternative hypotheses.

b.What is the test statistic from the ANOVA table?

c.With ? = 0.05, what is the critical value?

d.At ? = .05, test to determine if there is a significant difference among the average incomes of the employees from the three departments. Use the critical value approach. Write out the decision rule.

Answer 1

a)null hypothesis:Ho: average incomes of the employees from the three departments are equal.

alternate hypotheiss: Ha: not all  three departments have equal average incomes of the employees

b)

test statistic from ANOVA table F =1.8

c)

critical value F=3.68

d)

deicision rule:reject Ho if test statistic F >3.68

as test statistic is not in critical region we can nnot reject null hypothesis

we do not have suffcient evidence to conclude that there is a significant difference among the average incomes of the employees from the three departments.