Question

an 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 60 days in each region. the mean wind speed in region a is 13.8 miles per hour. assume the population standard deviation is 2.9 miles per hour. the mean wind speed in region b is 15.1 miles per hour. assume the population standard deviation is 3.1 miles per hour. at α = 0.05, can the company support the researcher’s claim? complete parts (a) through (d) below.

let region a be sample 1 and let region b be sample 2. identify ( h_0 ) and ( h_a ).
( h_0: mu_1 geq mu_2 )
( h_a: mu_1 < mu_2 )
(b) find the critical value(s) and identify the rejection region.
the critical value(s) is/are ( z_0 = -1.64 ).
(round to two decimal places as needed. use a comma to separate answers as needed.)
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 < square ) or ( z > square )
b. ( z < square )
c. ( z > square )

Explanation:

Step1: Determine Test Type

This is a left - tailed z - test (since we are testing if $\mu_1<\mu_2$ and population standard deviations are known). For a left - tailed test with $\alpha = 0.05$, we look for the z - value that separates the lower 5% of the standard normal distribution.

Step2: Find Critical Value and Rejection Region

The critical value for a left - tailed test with $\alpha=0.05$ is $z_0=- 1.64$ (from standard normal distribution tables, the z - score corresponding to a cumulative probability of 0.05 in the left tail is - 1.64). In a left - tailed test, the rejection region is the set of z - scores that are less than the critical value. So the rejection region is $z < - 1.64$. So we choose option B and fill in - 1.64.

Answer:

B. $z < - 1.64$