Question

A simple random sample of size n is drawn from a population that is known to be normally distributed. The sample​ variance, s squared​, is determined to be 13.4. Complete parts​ (a) through​ (c). ​(a) Construct a​ 90% confidence interval for sigma squared if the sample​ size, n, is 20. The lower bound is nothing. ​(Round to two decimal places as​ needed.) The upper bound is nothing. ​(Round to two decimal places as​ needed.) ​(b) Construct a​ 90% confidence interval for sigma squared if the sample​ size, n, is 30. The lower bound is nothing. ​(Round to two decimal places as​ needed.) The upper bound is nothing. ​(Round to two decimal places as​ needed.) How does increasing the sample size affect the width of the​ interval? The width increases The width does not change The width decreases ​(c) Construct a​ 98% confidence interval for sigma squared if the sample​ size, n, is 20. The lower bound is nothing. ​(Round to two decimal places as​ needed.) The upper bound is nothing. ​(Round to two decimal places as​ needed.) Compare the results with those obtained in part​ (a). How does increasing the level of confidence affect the confidence​ interval? The width increases The width decreases The width does not change Click to select your answer(s).

Answer 1

Given information:

(a)

Degree of freedom:

df=n-1=19

For 90% confidence interval value critical value of chi sqaure statitics will be

The confidence interval for the population variance is

(b)

Degree of freedom:

df=n-1=29

For 90% confidence interval value critical value of chi sqaure statitics will be

The confidence interval for the population variance is

(c)

Degree of freedom:

df=n-1=19

For 98% confidence interval value critical value of chi sqaure statitics will be

The confidence interval for the population variance is

How does increasing the level of confidence affect the confidence​ interval?

The width increases.