Are the mean annual wages the same for all three cities? Use \(\alpha=0.10\). Assume that the population variances are equal.

(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,

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

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

Use the data, which list the annual wages (in thousands of dollars) for randomly selected individuals from three metropolitan areas. Assume the wages are normally distributed and that the samples are independent.

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Ithaca, NY: 44.2, 51.5, 25.8, 28.3, 37.8, 38.0, 32.6, 41.8, 42.0, 40.6, 26.2, 27.9, 48.3. Little Rock, AR: 45.1, 38.1, 47.8, 34.4, 39.6, 47.1, 29.6, 54.8, 34.4, 40.3, 40.1, 41.7, 40.9, 38.9, 25.9 Madison, WI: 50.3, 41.8, 55.5, 40.8, 55.6, 38.6, 50.0, 46.8, 49.0, 52.9, 48.3, 47.5, 39.2, 32.7, 54.1