QuestionAn energy company wants to choose between two regions in a state to install energy-producing wind turbines. A researcher claims that the wind speed in Region $A$ is less than the wind speed in Region $B$. To test the regions, the average wind speed is calculated for 90 days in each region. The mean wind speed in Region A is 14.1 miles per hour. Assume the population standard deviation is 2.8 miles per hour. The mean wind speed in Region B is 15.3 miles per hour. Assume the population standard deviation is 3.2 miles per hour. At $\alpha=0.05$, can the company support the researcher's claim? Complete parts (a) through (d) below. D. The wind speed in Region A is less than the wind speed in Region B.
Let Region $A$ be sample 1 and let Region $B$ be sample 2. Identify $H_{0}$ and $H_{a}$. $$\begin{array}{l} H_{0}: \mu_{1} \geq \mu_{2} \\ H_{a}: \mu_{1}<\mu_{2} \end{array}$$ (b) Find the critical value(s) and identify the rejection region.
The critical value(s) is/are $z_{0}=$ $\square$ (Round to two decimal places as needed. Use a comma to separate answers as needed.)