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 60days in each region. The mean wind speed in Region A is 13.7 miles per hour. Assume the population standard deviation is 2.8miles per hour. The mean wind speed in Region B is 15.1miles per hour. Assume the population standard deviation is 3.2 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 the Ho and Ha What is the claim?

B. Find the critical value(s) and identify the rejection region. The critical value(s) is/are Zo= What is the rejection region? (Example: Z is ____ <,>< and >)

C. Find the test statistic z. Z= round to 2 decimal places

D. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. _________Ho. There_____ enough evidence at the ___% level of significance to ____ the researcher's claim that the wind speed in Region A is _______ the wind speed in Region B

Answer 1

We have given that

For Speed of Region A: X1bar = 13.7    σ1 = 2.8   n1= 60

For Speed of Region B: X2bar = 15.1    σ2 = 3.2 n2 = 60

We want to test the claim that the wind speed in Region A is less than the wind speed in Region B.

1. The hypotheses are

H₀ : μ₁ ≥ μ₂

H_a : μ₁ < μ₂

The population standard deviations are known so we are using two sample Z test.

2. The critical value is Z₀ = Z_0.05 = -1.96

The rejection region for this left tailed test is R = { z : z < -1.96}

3. Test statistics:

Z= (X1bar-X2bar) - ( μ₁ – μ₂) /

Z = (13.7 - 15.1)/SQRT((2.8^2)/60 + (3.2^2)/60)

Test statistics Z = -2.55

4. Since test statistics z = -2.55 < -1.96 so, we reject H₀.

We can conclude that the there is enough evidence at the 5% level of significance to support the research’s claim that the wind speed in region A is less than the wind speed in Region B.