Question

11, a A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x overbarx​, is found to be 102​, and the sample standard​ deviation, s, is found to be 10.

​(a) Construct a 96​% confidence interval about muμ if the sample​ size, n, is 24.

​(b) Construct a 96​% confidence interval about muμ if the sample​ size, n, is 17.

​(c) Construct a 90​% confidence interval about muμ if the sample​ size, n, is 24.

​(d) Should the confidence intervals in parts​ (a)-(c) have been computed if the population had not been normally​ distributed?

​(a) Construct a 96​% confidence interval about muμ if the sample​ size, n, is 24.

Lower​ bound: ___​; Upper​ bound: ____

​(Round to one decimal place as​ needed.)

​(b) Construct a 96​% confidence interval about muμ if the sample​ size, n, is 17.

Lower​ bound: ___​; Upper​ bound: ___

​(Round to one decimal place as​ needed.)

How does decreasing the sample size affect the margin of​ error, E?

A.

As the sample size​ decreases, the margin of error stays the same.

B.

As the sample size​ decreases, the margin of error decreases.

C.

As the sample size​ decreases, the margin of error increases.

​(c) Construct a 90​% confidence interval about muμ if the sample​ size, n, is 24.

Lower​ bound: ___​; Upper​ bound: ____

​(Round to one decimal place as​ needed.)

Compare the results to those obtained in part​ (a). How does decreasing the level of confidence affect the size of the margin of​ error, E?

A.

As the level of confidence​ decreases, the size of the interval stays the same.

B.

As the level of confidence​ decreases, the size of the interval decreases.

C.

As the level of confidence​ decreases, the size of the interval increases.

​(d) Should the confidence intervals in parts​ (a)-(c) have been computed if the population had not been normally​ distributed?

A.

​No, the population needs to be normally distributed because each sample size is less than 30.

B.

​Yes, the population does not need to be normally distributed because each sample size is small relative to their respective population sizes.

C.

​No, the population needs to be normally distributed because each sample size is large relative to their respective population sizes.

D.

​Yes, the population does not need to be normally distributed because each sample size is less than 30.

Answer 1