A channel claims that the mean amount of money spent by a family at movie theaters is greater than the mean amount spent by a family at amusement parks. The results for samples of expenses for the two modes of entertainment are shown at the left. At \(\alpha=0.01\), can you support the channel's claim? Assume the population variances are equal.

(a) identify the claim and state H₀ and H_a,

(b) find the critical value(s) and identify the rejection region(s),

(c) find the standardized test statistic t,

(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, and the populations are normally distributed.

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Sample Statistics for Amount Spent by Customers Movies Amusement Parks X = $86 = $1 $9 n1 n = 26 = $82 $1 = $7 n1 36 =