A travel agency claims that the average daily cost of meals and lodging for vacationing in Alaska is greater than the average daily cost in Colorado. The table given below shows the results of a random survey of vacationers in each state. The two samples are independent. Assume that σ₁ = $24 for Alaska and σ₂ = $19 for Colorado, and that both populations are normally distributed. At α = 0.05, is there enough evidence to support the claim? [H₀: μ₁ ≤ μ₂ and H_a: μ₁ > μ₂ (claim)]

a. Use technology to find the test statistic or the P-value.

b. Decide whether to reject the null hypothesis.

c. Interpret the decision in the context of the original claim.

Sample Statistics for Daily Cost of Meals and Lodging for Two Adults

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Alaska Colorado $296$293 n 15 20