An energy company wants to choose between two regions in a state to install ener
ID: 3200754 • Letter: A
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 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 15.4 miles per Assume the population standard deviation is 3.2 miles per hour. At alpha = 0.05, can the company support the researcher's claim? Complete parts (a) through below. Identify the claim and state H_0 and H_a What is the claim? The wind speed in Region A is less than the wind speed in Region B The wind speed in Region A is not less than the wind speed in Region B The wind speed in Region A is the same as the wind speed in Region B The wind speed in Region A is not greater than the wind speed in Region B Let Region A be sample 1 and let Region B be sample 2. ldentify H_0 and H_a:mu_1 mu_2 H_a: mu_1 mu_2 Find the critical value(s) and identify the rejection region. The critical value(s) is/are z_0 = (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.) z > z zExplanation / Answer
Solution:-
a) (A)The claim is that wind speed in region A is less than the wind speed in region B.
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: A> B
Alternative hypothesis: A < B
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample z-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), and the z statistic test statistic (z).
b) zcritical
z0 = - 1.65
Rejection region is:-
z < -1.65
SE = sqrt[(s12/n1) + (s22/n2)]
SE = sqrt[(2.72/60) + (3.22/60]
S.E = 0.54052
z = [ (x1 - x2) - d ] / SE
c) z = - 3.15
z value of the test is less than the critical value so we have to reject the null hypothesis.
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means (115) produced a z statistic of - 3.145. We use the z Distribution Calculator to find P(z < -3.145) = 0.00080.
Therefore, the P-value in this analysis is 0.00080.
d) Interpret results. Since the P-value (0.00080) is less than the significance level (0.05), we have reject the null hypothesis.
From this we can conclude that we have sufficient evidence in the favor of the claim that wind speed in region A is less than the wind speed in region B.