Question

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x​, is found to be 111​, and the sample standard​ deviation, s, is found to be 10.

​(a) Construct an 80​% confidence interval about μ if the sample​ size, n, is 14.

​(b) Construct an 80​% confidence interval about μ if the sample​ size, n, is 29.

​(c) Construct a 95​% confidence interval about μ if the sample​ size, n, is 14.

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

_______________________________________________________________

​(a) Construct an 80​% confidence interval about μ if the sample​ size, n, is 14.

Lower​ bound:__

Upper​ bound: __

​(Use ascending order. Round to one decimal place as​ needed.)

​(b) Construct an 80​% confidence interval about μ if the sample​ size, n, is 29.

Lower​ bound:_

Upper​ bound:_

​(Use ascending order. Round to one decimal place as​ needed.)

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

A.) As the sample size increases​, the margin of error increases.

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

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

​(c) Construct a 95​% confidence interval about μ if the sample​ size, n, is 14.

Lower​ bound:__

Upper​ bound: __

​(Use ascending order. Round to one decimal place as​ needed.)

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

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

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

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

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

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

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

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

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

A. ​No, the population does not need to be normally distributed.

B. ​Yes, the population needs to be normally distributed.

C. ​No, the population needs to be normally distributed.

D. ​Yes, the population does not need to be normally distributed.

Answer 1

Solution:-

(a) 80​% confidence interval about μ if the sample​ size, n, is 14.

lower bound : 107.4

upper bound : 114.6

(b) 80​% confidence interval about μ if the sample​ size, n, is 29

lower bound : 108.6

upper bound : 113.4

=> option B.

(c) 95​% confidence interval about μ if the sample​size, n, is 14

Lower bound : 105.2

upper bound : 116.7

=> option C. As the level of confidence increases​, the size of the interval increases.

=> option B.