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 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 15.1 miles per hour. Assume the population standard deviation is 3.2 miles per hour. At a = 0.05, can the company support the researcher's claim? Complete parts (a) through (d) below.

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(a) Identify the claim and state
H0
and
Ha.
 
What is the​ claim?
Let Region A be sample 1 and let Region B be sample 2. Identify
H0
and
Ha.
(b) Find the critical​ value(s) and identify the rejection region.​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)
What is the rejection​ region?
​(c) Find the standardized test statistic z.(Round to two decimal places as​ needed.)
​(d) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.
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 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 15.1 miles per hour. Assume the population standard deviation is 3.2 miles per hour. At a = 0.05, can the company support
the researcher's claim? Complete parts (a) through (d) below.
Transcribed Image Text: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 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 15.1 miles per hour. Assume the population standard deviation is 3.2 miles per hour. At a = 0.05, can the company support the researcher's claim? Complete parts (a) through (d) below.
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