A researcher wants to determine whether there is a difference in the hourly pay rates for registered nurses in Indiana, Kentucky, and Ohio. The researcher randomly selects several registered nurses in each state and records the hourly pay rate for each. The table shows the results. At \(\alpha=0.05\), can the researcher conclude that the distribution of the hourly pay rates of registered nurses in at least one state is different from the others?

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

(b) find the critical value and identify the rejection region,

(c) find the test statistic \(H,\) 

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

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

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State Annual salary (in thousands of dollars) Kentucky 39.9 41.6 50.5 62.1 38.3 32.9 39.9 North Carolina 48.8 47.2 41.9 59.6 40.8 44.9 48.8 South Carolina 35.4 43.0 49.1 48.5 40.3 41.7 35.4 West Virginia 34.8 45.9 36.6 45.1 50.3 38.1 34.8