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Just looking for worked out solution to D & E. (B & C just given for aid in solv

ID: 3366055 • Letter: J

Question

Just looking for worked out solution to D & E. (B & C just given for aid in solving).

B. [1.379,1.784]

C. [0.0569,0.245]

D. [-0.00875,0.1021]

4) The efficiency of two new 600 kW wind turbines is being analyzed. Both turbines were installed at 12 sites throughout Denmark, and the annual energy outputs was recorded as follows, in GWh/year; 1 23 4 5 678 9 10 12 Site Turbine 11.20 1.65 1.14 1.40 2.10 2.00 1.60 142 1.37 135 1.90 1.85 Turbine 2 1.24 1.60 1.15 1.32 2.15 193 1.58 134 1.35 1.10 1.76 1.90 a) Can these two samples be treated as independent? Why or why not? b) Construct a 95% confidence interval on the mean annual energy output of turbine 1. c) Construct a 90% confidence interval on the variance of the mean annual energy output of turbine 1 d) Construct a 95% confidence interval on the difference in the mean annual energy outputs. e) Is there any indication that one turbine is more efficient than the other?

Explanation / Answer

D) for turbine 1

X1 = 1.58, s1 = 0.32, n1 = 12

For turbine 2

X2 = 1.54, s2 = 0.34, n2 = 12

SE = sqrt (s12/n1 + s22/n2)

= sqrt ((0.32)^2/12 + (0.34)^2/12)

= 0.135

DF = ((0.32)^2/12 + (0.34)^2/12)^2 / (((0.32)^2/12)^2/11 +((0.34)^2/12)^2/11) = 21.91 = 22

With 22 degrees of freedom and 95% confidence interval the critical value is 2.074

Confidence interval is

(x1 - x2) +/- t* * SE

= (1.58 - 1.54) +/- 2.074 * 0.135

= 0.04 +/- 0.27999

= -0.23999, 0.31999

E) As the mean of first turbine is greater than the mean of second turbine , so first is more efficient.