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
[tex] \bf [ \bar x-z^*\frac{s}{\sqrt n}, \bar x+t^*\frac{s}{\sqrt n}][/tex]
where
[tex] \bf \bar x[/tex]= 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 [tex]\bf z^*[/tex] 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
[tex] \bf [26.7-1.96*\frac{17.7}{\sqrt{180}}, 26.7+1.96*\frac{17.7}{\sqrt{180}}]=\boxed{[24.114,29.2858]}[/tex]
(*)
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
