Answer:
a)  
 
Now we just take square root on both sides of the interval and we got:
 
b) For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56 
Step-by-step explanation:
423.6, 487.3, 453.2, 402.9, 483.0, 477.7, 442.3, 418.4, 459.0
Part a
The confidence interval for the population variance is given by the following formula:
 
On this case we need to find the sample standard deviation with the following formula:
![s=sqrt{\frac{\sum_{i=1}^8 (x_i -\bar x)^2}{n-1}}
And in order to find the sample mean we just need to use this formula:
[tex]\bar x =\frac{\sum_{i=1}^n x_i}{n}](https://tex.z-dn.net/?f=s%3Dsqrt%7B%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5E8%20%28x_i%20-%5Cbar%20x%29%5E2%7D%7Bn-1%7D%7D%0A%3C%2Fp%3E%3Cp%3EAnd%20in%20order%20to%20find%20the%20sample%20mean%20we%20just%20need%20to%20use%20this%20formula%3A%0A%3C%2Fp%3E%3Cp%3E%5Btex%5D%5Cbar%20x%20%3D%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20x_i%7D%7Bn%7D) 
The sample deviation for this case is s=30.23
The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:
 
The Confidence interval is 0.98 or 98%, the value of  and
 and  , and the critical values are:
, and the critical values are:
 
 
And replacing into the formula for the interval we got:
 
 
Now we just take square root on both sides of the interval and we got:
 
Part b
For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56