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
8	19	18
13	15	11
17	24	20
10	14	18
16	20	20
19	24	13
15	17	15
8	11	13

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.

Step 2 of 2:

Make the decision to reject or fail to reject the null hypothesis of equal average hourly wages in the three areas and state the conclusion in terms of the original problem. Use α=0.01.

Answer 1

For the given data using Anova single factor in Excel we get output as

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Area 1	8	106	13.25	17.64286
Area 2	8	144	18	21.71429
Area 3	8	128	16	12
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	91	2	45.5	2.657858	0.09355	5.780416
Within Groups	359.5	21	17.11905
Total	450.5	23

So from the above output

F = ms between / ms within

F = 45.5 / 17.11905

F = 5.78

value of the test statistic = 2.66

Decision :

At   α=0.01 l.o.s , df = ( 2,21 )

F critical value = 5.78

f cal < f crit

i.e., 2.66 < 5.78

so fail to reject the null hypothesis