Question

[Should we build a wind farm?] Wind Power has been the most popular alternative energy choice in recent years. One of the key determinants for choosing a location for a wind farm is whether the site has enough wind. To produce enough energy using current technology, the site should have an annual average wind speed exceeding 9.25 miles per hour, according to the Wind Energy Association. One candidate site in southern California was monitored for a year, with wind speeds recorded every 6 hours. A total sample of 1074 reading of wind speed averaged 9.487 mph with a sample standard deviation of 5.762 mph. The histogram of these 1074 readings is shown below. You are asked to perform statistical analysis to help the developer decide whether to place a wind turbine at this site. Use this information to answer questions 10 to 13. 140 120 100 Aanba 80 60 40 20 0 Wind Speed Figure 1: Histogram of Wind Speed at a candidate location

Answer 1

(10)

Parameter: Annual average wind speed

Hypotheses are: H: = 9.25 H:\> 9.25

(11)

Level of significance: a =0.05 Test is one tailed (right tailed). Degree of freedom: df =n-1=1073 Test Statistics: K- t= = (9.487-9.25)/(5.762/sqrt(1074)) sin = 1.348 Critical value: Rejection Region: 1.646 If t > 1.646, Reject HO Decision: Since test statistics does not lie in rejection region so we fail to reject the null hypothesis P-value: P-value=0.089 Decision: Since p-value is not less than level of significance so we fail to reject the null hypothesis Excel function for critical value: Excel function for p-value: TINV(0.1,1073) =TDIST(1.348,1073,1)

(12)

Conclusion: Fail to reject the null hypothesis

Interpretation: There is no evidence to conclude that wing speed is more than 9.25 miles per hour. So you should not recommend the building farm at that site.

(13)

As the level of significance increases chances of rejecting the null hypothesis also increases.

New significance level:

a = 0.10

Conclusion: Since p-value is less than 0.10 so reject the null hypothesis

Interpretation: There is evidence to conclude that wing speed is more than 9.25 miles per hour. So you should recommend the building farm at that site.