Question

a climatologist claims that the precipitation in seattle, washington, was greater than in birmingham, alabama, in a recent year. the daily precipitation amounts (in inches) for 30 days in a recent year in seattle and a recent year in birmingham are given in the accompanying table. assume the population standard deviation is 0.247 inch for seattle and 0.523 inch for birmingham. at α = 0.05, can you support the climatologist’s claim? complete parts (a) through (e). click the icon to view the precipitation data. b. z > 1.64 c. z < or z > (c) find the standardized test statistic z. z = -1.02 (round to two decimal places as needed.) (d) decide whether to reject or fail to reject the null hypothesis. the p - value is 0.846. (round to three decimal places as needed.) fail to reject h₀ because the p - value is greater than α = 0.05. (e) interpret the decision in the context of the original claim. there enough evidence at the 5% level of significance to the climatologist’s claim that the mean precipitation in seattle in birmingham in a recent year.

Explanation:

To interpret the decision, we recall that we failed to reject the null hypothesis (since \( P\text{-value} = 0.846 > \alpha = 0.05 \)). This means there is not enough evidence to support the alternative hypothesis (the climatologist’s claim). So, we fill in the blanks: "There is not enough evidence at the 5% level of significance to support the climatologist’s claim that the mean precipitation in Seattle is greater than in Birmingham in a recent year."

Answer:

There is not enough evidence at the 5% level of significance to support the climatologist’s claim that the mean precipitation in Seattle is greater than in Birmingham in a recent year.