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 13.9 miles per hour. Assume the population standard deviation is 2.8 miles per hour. The mean wind speed in Region B is 15.2 miles per hour. Assume the population standard deviation is 3.3 miles per hour. At alphaequals0.05​, can the company support the​ researcher's claim? Complete parts​ (a) through​ (d) below. ​

(a) Identify the claim and state Upper H 0 and Upper H Subscript a.

What is the​ claim?

A. The wind speed in Region A is not greater than the wind speed in Region B.

B. The wind speed in Region A is the same as the wind speed in Region B.

C. The wind speed in Region A is not less than the wind speed in Region B.

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 Upper H 0 and Upper H Subscript a.

Upper H 0​: mu 1 ▼ greater than or equals not equals less than or equals greater than less than mu 2

Upper H Subscript a​: mu 1 ▼ less than greater than greater than or equals not equals less than or equals mu 2 ​

(b) Find the critical​ value(s) and identify the rejection region.

The critical​ value(s) is/are z 0equals = .

​(Round to three 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 three decimal places as​ needed.)

A. z less than =   or z greater than =

B. z greater than =

C. z less than =​

(c) Find the standardized test statistic z. zequals = ​(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.

▼= ( Fail to reject ,Reject) Upper H 0. There ▼= (is ,not is) enough evidence at the 5​% level of significance to ▼= (support ,reject) the​ researcher's claim that the wind speed in Region A is ▼= (not greater than, less than not less than ,the same as) the wind speed in Region B. Click to select your answer(s).

Answer 1

(a) The null and alternative hypothesis is ,

(Claim)

The test is one-tailed test.

Claim : D. The wind speed in Region A is less than the wind speed in Region B.

(b) The critical value is ,

; From Z-table

Rejection region : C. Z < -1.645

(c) The standardized test statistic is ,

(d) Decision : Here , Z-stat=-2.33<-1.645

Therefore , reject Ho.

Conclusion : There is enough evidence at the 5% level of significance to support the researcher's claim that the wind speed in Region A is less than the wind speed in Region B.