Question

Should you generate electricity with our own personal wind turbine? That depends on whether you have enough wind on your site. To produce enough energy, your site should have an annual average wind speed above 8 miles per hour, according to the Wind Energy Association. One candidate site was monitored for a year, with wind speeds recorded every 6 hours. A total of 1114 readings of wind speed averaged 8.019mph (assume a population standard deviation wind speed of 3.813). You’ve been hired to produce a statistical report to help this landowner decide if he should build a turbine.

Answer 1

To solve this problem, first we have to determine the z statistic. The formula is

$z= \frac{x-mean}{s \sqrt{n} }$

where x is the test point which is 8.019, the mean is 8 mph, s is the standard deviation which is 3.813 and n is the number of data which is 1114. Then,

$z= \frac{8.019-8}{ \frac{3.813}{ \sqrt{1114}} }= 0.17$

Next, we find the p-value for the particular z. p-value is used in hypothetical test. Using a wind turbine would be the null hypothesis. From the standard normal table found in any statistics book, the p-value for z<0.17 is 0.5675. If the p-value is greater than 0.05, then you do not reject the null hypothesis.

Therefore, the landowner could use a small turbine at the site.