Question

Should you generate electricity with your own personal wind turbine? That depends on whether you have the right amount of wind on your site. For a personal wind turbine to work properly, your site should have an annual average wind speed of at least 10 miles per hour, according to the Wind Energy Association. Lower winds do not provide enough energy. One candidate site was monitored last year, with wind speeds recorded every 8 hours. A total of 49 readings of wind speeds average 9.56 mph with a standard deviation of 2.52 mph. You've been asked to make a statistical report to help the landowner decide whether to place a wind turbine at the site.

At the .05 level of significance, the site (is / is not) suitable for a small wind turbine.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 10
Alternative Hypothesis, Ha: μ < 10

Rejection Region
This is left tailed test, for α = 0.05 and df = 48
Critical value of t is -1.677.
Hence reject H0 if t < -1.677

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (9.56 - 10)/(2.52/sqrt(49))
t = -1.222

P-value Approach
P-value = 0.1138
As P-value >= 0.05, fail to reject null hypothesis.

At the .05 level of significance, the site ( is not) suitable for a small wind turbine.