Question

A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 25 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. Based on a sample of 43 wind speed recordings (taken at random intervals), the wind speed at the site averaged 25.8 mph, with a population standard deviation of 4.2 mph

a. Construct a 95% confidence interval for the mean wind speed

b. Calculate the p−value of the test statistic

c. Test whether the site meets the organization’s requirements at the 5% level of significance

Answer 1

Part a)

Confidence Interval :-



Lower Limit =
Lower Limit = 24.5447
Upper Limit =
Upper Limit = 27.0553
95% Confidence interval is ( 24.5447 , 27.0553 )

Part b)

P value = P ( Z > 1.249 ) = 0.1058

Part c)

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


Z = 1.249

Test Criteria :-
Reject null hypothesis if


Result :- Fail to reject null hypothesis

Accept Null Hypothesis

There is insufficient evidence to support the claim that the organization meets requirements at the 5% level of significance