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 21 10 15 21 24 11 24 18 18 17 22 14 15 22 15 18 16 14 11 24 12 22 21 16 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

Hourly Wages $
Area 1	Area 2	Area 3
21	10	15
21	24	11
24	18	18
17	22	14
15	22	15
18	16	14
11	24	12
22	21	16

Anova: Single Factor

One-way ANOVA: Area 1, Area 2, Area 3

Method

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.

Factor Information

Factor	Levels	Values
Factor	3	Area 1, Area 2, Area 3

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	2	124.3	62.17	4.08	0.032
Error	21	319.6	15.22
Total	23	444.0

test statistic F = 4.08

for a given significance level of 0.05, p-value is less than 0.05, we reject null hypothesis at alpha = 0.05, and there is a significant evidence to conclude that the hourly wages differ between the areas.

Tukey Simultaneous Tests for Differences of Means

Difference of Levels	Difference of Means	SE of Difference	95% CI	T-Value	Adjusted P-Value
Area 2 - Area 1	1.00	1.95	(-3.91, 5.91)	0.51	0.866
Area 3 - Area 1	-4.25	1.95	(-9.16, 0.66)	-2.18	0.098
Area 3 - Area 2	-5.25	1.95	(-10.16, -0.34)	-2.69	0.035

Individual confidence level = 98.00%

Area 2 and Area 3 are significantly differ.