At \(\alpha=0.01\), is there enough evidence to conclude that the variances of the annual wages for Ithaca, NY, and Little Rock, AR, are different?

(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