Question

NASA has been working with utility companies to set up expensive power generating windmills. In order for a site to be effective, the average wind speed must be more than 20 mph. At a specific site, NASA took a sample of forty-five wind speed readings. The sample average wind speed is 21.7 mph with a standard deviation of 4.2 mph. NASA will only build the windmill if they are sure that the true average wind speed is greater than 20 mph. Should they build the windmill? Justify by conducting a hypothesis test at α = 0.05.

Answer 1

This is the right tailed test .

The null and alternative hypothesis is

H₀ : = 20

H_a : > 20

Test statistic = t

= ( - ) / s / n

= (21.7 - 20) / 4.2 / 45

= 2.715

Test statistic = 2.715

df = 44

P-value = 0.0047

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to conclude that the true average wind speed is greater than 20 mph