The table shows the prices (in dollars) for a sample of automobile batteries. The prices are classified according to battery type. At α = 0.05, is there enough evidence to conclude that at least one mean battery price 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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Group size 35 110 100 280 145 180 125 90 120 Group size 65 175 90 140 140 Group size 24/24F 125 85 80