Need help with a statistics problem!?
Should you generate electricity with your own personal wind turbine? The answer depends on whether your site has sufficient wind resources. According to the Wind Energy Association, to produce enough energy, your location should have an annual average wind speed exceeding 8 miles per hour. One candidate site was monitored for a year, with wind speeds recorded every six hours. A total of 1,114 readings of wind speed averaged 8.019 mph, with a standard deviation of 3.813 mph.
You have been asked to prepare a statistical report to help the landowner decide whether to install a wind turbine at this site.
a) Discuss the assumptions and conditions necessary for using Student's t inference methods with this data.
b) What would you advise the landowner regarding the suitability of this site for a small wind turbine? Please explain your reasoning.
Any assistance would be greatly appreciated! Thank you.
1 Answers
Jan 20, 2025
Brooke
a) Discuss the assumptions and conditions for using Student's t inference methods with this data.
The samples being compared should have a reasonably symmetrical distribution;
The samples being compared should have a mean which is close to the center of the distribution:
The distribution should have only one mode (highest point in the frequency histogram).
However, since n is very large (1114), you can safely use a Standard Normal table.
b) What would you tell the landowner about whether this site is suitable for a small wind turbine? Explain.
Ho: mean = 8
Ha: mean < 8
z-statistic = (8.018 - 8) / (3.813 / sqrt 1114) = 0.16
P-value = P(z < 0.16) = 0.5636 [from Standard Normal table]
Since the P-value is very large (>0.05), do NOT reject the null hypothesis. Tell the landowner to place a wind turbine at the site.
hope that helped
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