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.

Test whether the average wind speed is at least 10 mph at the .025 level of significance.

Show Your Work! Formula(s), Substitutions, Answers! Round your critical value to 3 decimal places, and your pvalue to 4 decimal places.

Answer 1

(7) = 1- (0.16 + 0.2 + 0.36) = 0.28

mean = 3 * 0.16 + 6 * 0.2 + 7 * 0.28 + 12 * 0.36

= 7.96

std.deviation = summation (sqrt(x - mean)^2*P(x))
= 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 = 0.025 and df = 48
Critical value of t is -2.011.
Hence reject H0 if t < -2.011

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 >= 0.025, fail to reject null hypothesis.