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

13.7

miles per hour. Assume the population standard deviation is

2.7

miles per hour. The mean wind speed in Region B is

15.3

miles per hour. Assume the population standard deviation is

3.1

miles per hour. At

alphaαequals=0.05,

can the company support the​ researcher's claim? Complete parts​ (a) through​ (d) below.​(a) Identify the claim and state

Upper H 0H0

and

Upper H Subscript aHa.

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 less than the wind speed in Region B.

D.

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

Let Region A be sample 1 and let Region B be sample 2. Identify

Upper H 0H0

and

Upper H Subscript aHa.

Upper H 0H0​:

mu 1μ1

▼

less than<

not equals≠

greater than>

greater than or equals≥

less than or equals≤

mu 2μ2

Upper H Subscript aHa​:

mu 1μ1

▼

less than or equals≤

less than<

greater than or equals≥

greater than>

not equals≠

mu 2μ2

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

The critical​ value(s) is/are

z 0z0equals=nothing.

​(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.

zless than<nothing

B.

zless than<nothing

or

zgreater than>nothing

C.

zgreater than>nothing

​(c) Find the standardized test statistic z.

zequals=nothing

​(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.

▼

Reject

Fail to reject

Upper H 0H0.

There

▼

is not

is

enough evidence at the

55​%

level of significance to

▼

support

reject

the​ researcher's claim that the wind speed in Region A is

▼

not greater than

less than

the same as

not less than

the wind speed in Region B.

Click to select your answer(s).

Answer 1

Given : For region A : , ,

For region B : , ,

Let , and be the population mean for region A and B respectively.

a) Hypothesis : Vs   ( Claim )

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

(b) The critical value is ,

; From the standard normal probability table

Rejection region is

Reject Ho if Z < - 1.645

(c) The standardized test statistic is ,

(d) Decision : Here , the value of the test statistic is lies in the rejection region .

Therefore , reject the null hypothesis.

Conclusion : Hence , there is enough evidence at the 5% level of significance to support the claim that the wind speed in Region A is less than the wind speed in Region B.