Question 9 Alternative sources of energy are of increasing interest throughout t

Question

Question 9 Alternative sources of energy are of increasing interest throughout the energy industry. Wind energy has great potential, but appropriate sites must be found for the turbines. To select the site for an electricity-generating wind turbine, wind speeds are recorded at several potential sites every six hours for a year. Two sites not far from each other looked good. Each had a mean wind speed high enough to qualify, but we should choose the site with a higher average daily wind speed

(a) Is there evidence that either of these sites has a higher average wind speed?

(b) Construct a 99% confidence interval for the mean difference in wind speeds.

Count Mean SD Site 2 1114 7.452 3.586 Site 4 1114 7.248 3.421 Site 2-Site 4 1114 0.204 2.551

Explanation / Answer

1 - 2 = (M1 - M2) ± ts(M1 - M2)

a)

an alpha of 0.05 is used as the cutoff for significance. the p-value is more than 0.05, we fail to reject the null hypothesis that there's no difference between the means and conclude that a significant difference does not exist

b)

[0.19253, 0.21547].

M1 & M2 = sample means
t = t statistic determined by confidence level
s(M1 - M2) = standard error = ((s2p/n1) + (s2p/n2))

1 - 2 = (M1 - M2) = 0.204, 99% CI [0.19253, 0.21547].

t-statistic -1.374

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