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.

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