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. a. the mean precipitation in seattle was greater than in birmingham in a recent year. b. the mean precipitation in seattle was less than in birmingham in a recent year. c. the mean precipitation in seattle was the same as in birmingham in a recent year. d. the mean precipitation in seattle was different than in birmingham in a recent year. let the data from seattle be sample 1 and let the data from birmingham be sample 2. identify h₀ and hₐ. h₀: μ₁ ≤ μ₂ hₐ: μ₁ > μ₂ (b) find the critical value(s) and identify the rejection region. select the correct choice below and fill in the answer box within your choice. (round to two decimal places as needed.) a. the critical value is z₀ = . b. the critical values are z₀ = ± .

Explanation:

Step1: Identify Test Type

This is a right - tailed z - test for two population means (since population standard deviations are known). For a right - tailed test with \(\alpha = 0.05\), we need to find the critical value \(z_0\) such that \(P(Z>z_0)=\alpha = 0.05\), or \(P(Z\leq z_0)=1 - \alpha=0.95\).

Step2: Use Z - table or Calculator

Looking up the z - value in the standard normal distribution table (z - table) for which the cumulative probability is 0.95. From the z - table, the z - value corresponding to a cumulative probability of 0.95 is approximately 1.645. Since it is a right - tailed test, we have one critical value. So we choose option A, and the critical value \(z_0 = 1.645\).

Answer:

A. The critical value is \(z_0=\boxed{1.645}\)