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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

6060

days in each region. The mean wind speed in Region A is

13.713.7

miles per hour. Assume the population standard deviation is

2.82.8

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

15.115.1

miles per hour. Assume the population standard deviation is

3.23.2

miles per hour. At

alphaαequals=0.050.05 ,

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 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 0H0

and

Upper H Subscript aHa.

Upper H 0H0 :

mu 1μ1

▼

greater than>

less than or equals≤

not equals≠

less than<

greater than or equals≥

mu 2μ2

Upper H Subscript aHa :

mu 1μ1

▼

greater than>

less than<

greater than or equals≥

less than or equals≤

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

or

zgreater than>nothing

B.

zgreater than>nothing

C.

zless 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.

▼

Fail to reject

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 less than

less than

not greater than

the same as

the wind speed in Region B.

Answer 1