The well-being index is a way to measure how people are faring physically, emotionally, socially, and professionally, as well as to rate the overall quality of their lives and their outlooks for the future. The table shows the well-being index scores for a sample of states from four regions of the United States. At α = 0.10, can you reject the claim that the mean score is the same for all regions?

(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,

(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. If convenient, use technology.

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Northeast Midwest South West 67.6 67.3 68.4 66.2 66.5 68.6 66.6 67.6 65.6 68.9 65.5 68.5 67.4 68.0 64.2 66.1 64.1 67.4 65.8 69.7 66.1 68.5 62.7 65.2 68.0 66.7 63.6 67.1 65.2 68.8 65.2 67.7 64.0 66.6