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An energy company wants to choose between two regions in a state to install energyproducing 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.
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