Question

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.

2. 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.

3. Interstate Batteries are supposed to last at least 3 years. A consumer advocate collects a random sample of 200 of these batteries and finds that 186 last at least 3 years. Does this provide evidence at the 5% significance level to support the claim that less than 95% of all Interstate batteries last at least 3 years? Justify by running a hypothesis test.

Answer 1

Answer:

For the right tailed test.

Null hypothesis H0 : U =20

Alternative Hypothesis U > 20

Test static t = (x' - U)/s/sqrt(n)

= (21.7 - 20)/4.2/sqrt(45)

=2.715

df = 44

p-value = 0.0047 (< p =0.05)

Reject Null hypothesis.

We have sufficient evidence that conclude true average wind speed is greater than 20 mph