Question

he number of hours of reserve capacity of 10 randomly selected automotive batteries is shown to the right. 1.71 1.88 1.57 1.67 1.78 1.99 1.37 1.54 1.44 2.04

Assume the sample is taken from a normally distributed population. Construct 95​% confidence intervals for​ (a) the population variance sigmasquared and​ (b) the population standard deviation sigma. ​

(a) The confidence interval for the population variance is ​( nothing​, nothing​). ​(Round to three decimal places as​ needed.) Interpret the results.

Select the correct choice below and fill in the answer​ box(es) to complete your choice. ​(Round to three decimal places as​ needed.)

A. With 95​% ​confidence, it can be said that the population variance is between nothing and nothing.

B. With 95​% ​confidence, it can be said that the population variance is less than nothing.

C. With 5​% ​confidence, it can be said that the population variance is between nothing and nothing.

D. With 5​% ​confidence, it can be said that the population variance is greater than nothing. ​

(b) The confidence interval for the population standard deviation is ​( nothing​, nothing​). ​(Round to three decimal places as​ needed.) Interpret the results.

Select the correct choice below and fill in the answer​ box(es) to complete your choice. ​(Round to three decimal places as​ needed.)

A. With 95​% ​confidence, you can say that the population standard deviation is between nothing and nothing hours of reserve capacity.

B. With 5​% ​confidence, you can say that the population standard deviation is between nothing and nothing hours of reserve capacity.

C. With 95​% ​confidence, you can say that the population standard deviation is less than nothing hours of reserve capacity.

D. With 5​% ​confidence, you can say that the population standard deviation is greater than nothing hours of reserve capacity.

Answer 1

Solution :-

For the given data, we have :

n = 10, s = 0.2257 is the sample standard deviation,

construct 95% confidence intrvals for (a) the population variance and (b) the population standard deviation.

Answer : The 95% confidence interval for the population variance is:

where :

is the chi-sqaure critical value at 0.05 significance level for df = n - 1 = 10 - 1 = 9.

Is the chi-square critical value at 0.975 significance level for df = n - 1 = 10 - 1 = 9.

Therefore, the 95% confidence interval for the population variance is (0.024, 0.170)

Interpret the resultes.

Answer : A. with 95% confidence, it can be said that the population variance is between 0.024 and 0.170.