Question

Directions: Read and answer each question carefully. Be sure to state your Ho and Ha, your test statistic and p-value, if you reject Ho, and your conclusion the words of the problem. Round to the thousandths place where applicable.

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.

B. For problem 1, Describe in the words of the problem what making a Type I error would be and its likely consequences. For problem 1, Describe in the words of the problem what making a Type II error would be and its likely consequences.

Answer 1

1. Null hypothesis : The Average wind speed at a specific location is 20 mph.

Alternative Hypothesis: The Average wind speed is more than 20 mph.

We are given that    and

Level of significance :

Test Statistic : follows at t with n-1 df.

Critical value of t=1.6794 obtained by T.INV.2T(0.1,45)(Please note that this function is a 2 tailed one and for getting the critical value for 1 tailed test, we need to find the value at 0.1)

Now

  

  . Since the calculated t(2.7152)>tabulated t(1.6794) we reject the null hypothesis. In other words, the p-value is p=0.0047 which is less than 0.05, we reject the null hypothesis.

Since this sample gives evidence to reject the hypothesis of 20 mph in favor of the alternative hypothesis that the wind speed is more than 20 mph, NASA can go ahead and build the windmill.

B. Making Type I error.

It is reject when it is true. This means in our context concluding that the wind speed is >20 mph and in reality it is only 20 mph. The consequence is that we should have gone ahead and build the windmill at that site where in fact the wind speed is not more than 20 mph(required for windmills). This will therefore not be able to generate any power and results in loss of erection cost and time.

Type II error: It is Accepting a Null hypothesis when it is false.

It is deciding that the wind speed is 20 mph when it is really more. We could have decided not to erect the windmill and in fact the wind speed is more than 20 mph. This will result in a long term loss or not tapping the potential in generating power.