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. what is the rejection region? select the correct choice below and fill in the answer box(es) within your choice. (round to two decimal places as needed.) a. z < 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.) h₀ because the p - value is α = 0.05.

Explanation:

Step1: Recall P - value decision rule

The decision rule for hypothesis testing using the P - value is: If \(P - value<\alpha\), we reject the null hypothesis \(H_0\); if \(P - value\geq\alpha\), we fail to reject the null hypothesis \(H_0\).

Step2: Compare P - value and \(\alpha\)

We are given that \(\alpha = 0.05\) and the \(P - value=0.846\). Since \(0.846>0.05\) (i.e., \(P - value\geq\alpha\)), we fail to reject the null hypothesis \(H_0\).

Answer:

Fail to reject \(H_0\) because the \(P\) - value is greater than \(\alpha = 0.05\).