Question

a.) what is the claim? identify H0 and Ha

b.) find the critical values and rejection region

c.) find the standarized test statistic z

An energy company wants to choose between two regions in a state to install new producing wind turbines Aresearcher claims that the wind speed in Region Ais 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 Als 13.8 miles per hour Assume the population standard deviation is 2.7 miles per hour. The mean wind speed in Region B is 15.2 miles per hour. Assume the population standard deviation is 32 miles per how At 0.05. Can the company support the researcher's claim? Complete parts (a) through (d) below (a) Identify the claim and state Hy and H What is the claim? O A The wind speed in Region Als the same as the wind speed in Region B OB. The wind speed in Region A is not less than the wind speed in Region B. OC. The wind speed in Region A is not greater than the wind speed in Region B OD. The wind speed in Region Ais less than the wind speed in Region Lot Region Abe sample 1 and lot Region B be sample 2. Identity Ho and H,

Answer 1

SOLUTION:

From given data,

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 13.8 miles per hour. Assume the population standard deviation is 2.7 miles per hour. The mean wind speed in Region B is 15.2 miles per hour. Assume the population standard deviation is 3.2 miles per hour. At $\alpha$ = 0.05. can the company support the researcher's claim?

a.) what is the claim? identify H₀ and H_a

What is the claim :

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

identify H₀ and H_a

Null hypothesis : H₀ : $\mu _{A}$ > $\mu _{B}$

Alternative hypothesis : H_a : $\mu _{A}$ < $\mu _{B}$ (Left tailed test)

b) Find critical value and identify the rejection region

level of significance $\alpha$ = 0.05

From the standard normal tables ,it is observed that the z-critical value at the 0.05 level of significance is -1.645.

Decision rule : Reject H₀ when Z_statistic < -1.645.

(c) Find the standardized test statistic z.

Calculate the test statistic value,

Z = ( $\bar{x}_{A}$ - $\bar{x}_{B}$ ) / sqrt($\sigma _{A}^{2}$ / + $\sigma _{B}^{2}$ / )

Z = ( 13.8 - 15.2) / sqrt((2.7)² / 60 + (3.2)² / 60 )

Z = -1.4 / 0.540524437

Z = - 2.590077

Z = - 2.59 (Rounded to two decimal places)

Hence , the required test statistics is - 2.59

Please thumbs-up / vote up this answer if it was helpful. In case of any problem, please comment below. I will surely help. Down-votes are permanent and not notified to us, so we can't help in that case.