Question

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x overbar ​, is found to be 106 ​, and the sample standard​ deviation, s, is found to be 10 . ​(a) Construct an 80 ​% confidence interval about mu if the sample​ size, n, is 29 .

​(b) Construct an 80 ​% confidence interval about mu if the sample​ size, n, is 13 . How does decreasing the sample size affect the margin of​ error, E?

​(c) Construct a 70 ​% confidence interval about mu if the sample​ size, n, is 29 . 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?

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

Answer 1