The table shows the salaries (in thousands of dollars) for a sample of individuals from the federal, state, and local levels of government. At α = 0.01, can you conclude that at least one mean salary is different from the others?

(a) Identify the claim and state H₀ and H_a, 

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

(c) Find the test statistic F, 

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

(e) Interpret the decision in the context of the original claim. Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal.

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Federal State Local 75.2 57.9 52.5 42.0 42.0 67.9 79.3 59.0 46.3 44.7 87.1 59.5 86.4 61.7 55.3 90.5 49.4 66.8 61.1 44.9 64.0 76.0 55.4 44.5 58.6 85.7 40.9 52.4 69.4 37.1