Question

A steel company is considering the relocation of one of its manufacturing plants. The company’s executives have selected four areas that they believe are suitable locations. However, they want to determine if the average wages are significantly different in any of the locations, since this could have a major impact on the cost of production. A survey of hourly wages of similar workers in each of the four areas is performed with the following results. Do the data indicate a significant difference among the average hourly wages in the three areas? Hourly Wages ($) Area 1 Area 2 Area 3 22 16 17 15 8 23 12 22 24 21 17 25 15 11 9 17 9 19 14 11 12 21 10 23 Step 1 of 2 : Find the value of the test statistic to test for a difference in the areas. Round your answer to two decimal places, if necessary.

Answer 1

Area 1	Area 2	Area 3
22	24	9
16	21	19
17	17	14
15	25	11
8	15	12
23	11	21
12	9	10
22	17	23

Method: One way Anova

Null hypothesis	All means are equal
Alternative hypothesis	Not all means are equal
Significance level	α = 0.05

Equal variances were assumed for the analysis.

Means

Factor	N	Mean	StDev	95% CI
Area 1	8	16.88	5.30	(12.84, 20.91)
Area 2	8	17.38	5.76	(13.34, 21.41)
Area 3	8	14.88	5.38	(10.84, 18.91)

Pooled StDev = 5.48428

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	2	28.00	14.00	0.47	0.634
Error	21	631.63	30.08
Total	23	659.63

Therefore the value of test statistics = 0.47

and p-value = 0.63

Decision: since the p-value is 0.63 which is quite large value. so we don't have sufficient evidence to reject the null hypothesis. So, Ho can't be rejected.

Conclusion: There is no significant difference among the average hourly wages in the three area.