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
1313	1919	88
88	1010	1111
1010	2323	1212
2121	2424	1919
1313	1414	1919
88	2222	1111
1111	2020	1717
1212	1313	99

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=0.10

a) We reject the null hypothesis. There is not sufficient evidence, at the 0.100.10 level of significance, of a difference among the average hourly wages in the three areas.

b) We fail to reject the null hypothesis. There is not sufficient evidence, at the 0.100.10 level of significance, of a difference among the average hourly wages in the three areas.

c)We fail to reject the null hypothesis. There is sufficient evidence, at the 0.100.10 level of significance, of a difference among the average hourly wages in the three areas.

d)We reject the null hypothesis. There is sufficient evidence, at the 0.100.10 level of significance, of a difference among the average hourly wages in the three areas.

Answer 1

To test against H₁ : at least one mean is different

Using Minitab software ( Stat -> ANOVA-> One way), we get the following output :

The value of F statistic = 3.96

and p-value = 0.035

Since p-value < 0.10, so we reject the null hypothesis at 10% level of significance and we can conclude that the average wages due to different areas are significantly different.

ans-> We reject the null hypothesis. There is sufficient evidence, at the 0.10 level of significance, of a difference among the average hourly wages in the three areas.