Question

Wind farm configuration is a significant issue as the upwind turbines generate maximal energy while creating wakes for downwind turbines. One measurement of interest is the wake expression parameter, WEP. A random sample of 180 WEP measurements in rescaled units has mean 26.7 and standard deviation 17.7. (a) Compute a 95% confidence interval for the true mean WEP. (b) Does the true mean WEP differ from 30? Explain.

Answer 1

Answer:

a) [24.114,29.2858]

b) Since 30 is not in the 95% confidence interval, there is a 95% probability that 30 is not the true mean WEP

Step-by-step explanation:

a)

The 95% confidence interval is given by the interval

$\bf [ \bar x-z^*\frac{s}{\sqrt n}, \bar x+t^*\frac{s}{\sqrt n}]$

where

$\bf \bar x$= 26.7 is the sample mean  

s = 17.7 is the sample standard deviation  

n = 180 is the sample size

Since the sample size is big enough, we can use the Normal N(0,1) to compute $\bf z^*$ and it would be 1.96(*) (a value such that the area under the Normal curve outside the interval [-z, z] is 5% (0.05))

and our 95% confidence interval is

$\bf [26.7-1.96*\frac{17.7}{\sqrt{180}}, 26.7+1.96*\frac{17.7}{\sqrt{180}}]=\boxed{[24.114,29.2858]}$

(*)

This value can be computed in Excel with

NORMINV(1-0.025,0,1)

and in OpenOffice Calc with

NORMINV(1-0.025;0;1)

b)

Since 30 is not in the 95% confidence interval, there is a 95% probability that 30 is not the true mean WEP