Are the mean hourly wages of respiratory therapist technicians the same for all three states? Use α = 0.01. Assume that the population variances are equal.

Use the data, which list the hourly wages (in dollars) for randomly selected respiratory therapy technicians from three states. Assume the wages are normally distributed and that the samples are independent.

Maine: 20.92, 25.37, 23.06, 15.64, 27.72, 24.90, 19.26, 23.46, 18.49, 21.76, 22.36

Oklahoma: 22.70, 19.95, 17.85, 16.76, 21.32, 18.96, 17.99, 28.35, 25.30, 21.93

Massachusetts: 25.43, 23.21, 30.81, 26.62, 31.42, 31.34, 34.58, 28.22, 27.25,22.83, 27.45, 27.71

(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,

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

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