An employment agency representative wants to determine whether there is a difference in the annual household incomes in four regions of the United States. The representative randomly selects several households in each region and records the annual household income for each. The table shows the results. At \(\alpha=0.01\), can the representative conclude that the distribution of the annual household incomes in at least one region is different from the others?

(a) identify the claim and state \(H_{0}\) and \(H_{a}\),

(b) decide which nonparametric test to use,

(c) find the critical value(s),

(d) find the test statistic,

(e) decide whether to reject or fail to reject the null hypothesis, 

(f) interpret the decision in the context of the original claim.

Transcribed Image Text:

Region Household income (in thousands of dollars) Northcast 64.2 57.0 65.6 64.7 59.9 62.4 61.5 Midwest 56.0 61.1 51.9 55.2 57.4 58.5 58.7 South 49.3 50.5 54.1 46.4 51.3 54.1 51.9 West 64.0 61.9 58.6 60.7 59.6 61.2 63.1