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}]](https://tex.z-dn.net/?f=%20%5Cbf%20%5B%20%5Cbar%20x-z%5E%2A%5Cfrac%7Bs%7D%7B%5Csqrt%20n%7D%2C%20%5Cbar%20x%2Bt%5E%2A%5Cfrac%7Bs%7D%7B%5Csqrt%20n%7D%5D)
where
= 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
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]}](https://tex.z-dn.net/?f=%20%5Cbf%20%5B26.7-1.96%2A%5Cfrac%7B17.7%7D%7B%5Csqrt%7B180%7D%7D%2C%2026.7%2B1.96%2A%5Cfrac%7B17.7%7D%7B%5Csqrt%7B180%7D%7D%5D%3D%5Cboxed%7B%5B24.114%2C29.2858%5D%7D)
(*)
This value can be computed in Excel with
<em>NORMINV(1-0.025,0,1)</em>
and in OpenOffice Calc with
<em>NORMINV(1-0.025;0;1)</em>
b)
Since 30 is not in the 95% confidence interval, there is a 95% probability that 30 is not the true mean WEP