Answer
$\bar{x}$ =$\frac{∑X}{n}$
=$\frac{557.7}{8}$
= 69.7125
s^2 = $\frac{ n(∑X^2) - [(∑X)^2] }{n(n-1)}$
= $\frac{312137.4- 311029.3}{8*7}$
=19.787
s = $ \sqrt 19.787 \ $
s =4.4483
n = 8, s = 4.4483 , df = 8-1=7, α = 1-0.99 = 0.01
To find χ2 right ,
α/2=0.005
From the table,
χ2 right = 20.278
To find χ2 left,
1-0.005=0.995
From the table,
χ2 left =0.989
The Confidence Interval for a Variance:
$ \frac{(n-1)s^2}{χ2 right}$
