Question

Explain a problem that might be solved using hypothesis testing. Would you use a one sample test or a two sample test and why? Run the problem in Megastat (using real or hypothetical data) and interpret the results.

Answer 1

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.

The hypothesis being tested is:

H0: µ = 20

Ha: µ > 20

The test statistic, t = (x - µ)/s/√n

t = (21.7 - 20)/4.2/√45 = 2.715

The p-value is 0.0047.

Since the p-value (0.0047) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the true average wind speed is greater than 20 mph.

Thus, they should not build the windmill.