Question

Question 2

An operations manager of a large firm is studying the monthly sales (in $’000) of three subsidiary companies over a six-month period as given in the table below.

Company A	Company B	Company C
152	148	150
135	158	148
130	136	126
142	138	128
125	140	140
128	127	135

At the 0.01 significance level, can we conclude that there is a difference in the means of monthly sales of the three subsidiary companies over a six-month period?

b)  Calculate the level of significance, critical value and rejection region

	A.	dfc = 5 dfe = 12 dft = 17 Critical Value: F0.005, 2, 12 = 6.93
	B.	dfc = 2 dfe = 15 dft = 17 Critical Value: F0.005, 2, 15 = 7.70
	C.	dfc = 2 dfe = 15 dft = 17 Critical Value: F0.01, 2, 15 = 6.36
	D.	dfc = 2 dfe = 15 dft = 17 Critical Value: F0.005, 2, 17 = 7.35

Answer 1

Ho :    
Ha : Atleast two population means differs from each other.

Level of Significance (l.o.s.) :   = 0.01

Decision Criteria : Reject Ho at 1% l.o.s. if F > F crit,
where F crit = F (, k-1, n-k) = F (0.01, 2,15) = 6.359

Calculation : To determine the results, we make use of Excel & the steps are :

Step 1 : Enter the data in excel.
Step 2 : Select "Anova : Single Factor" function fro the data analysis package available under the data tab of excel.
Step 3 : Enter the range of the data in the first cell & change the l.o.s. from 0.05 to 0.01
Step 4 : Click ok & thus, following results are obtained :

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Company A	6	812	135.3333333	102.2666667
Company B	6	847	141.1666667	113.7666667
Company C	6	827	137.8333333	100.1666667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	102.7777778	2	51.38888889	0.487560616	0.62352407	6.359
Within Groups	1581	15	105.4
Total	1683.777778	17

i.e. option C.

Conclusion : Since F < F crit, we do not reject Ho at 1% l.o.s. & thus, conclude that there is no significant difference in the means of monthly sales of the three subsidiary companies over a six-month period.

Hope this answers your query!