Question

A simple random sample of size n is drawn. The sample​ mean, x ​, is found to be 18.5 ​, and the sample standard​ deviation, s, is found to be 4.3.

(a) Construct a 95​% confidence interval about mean if the sample​ size, n, is 35.

(b) Construct a 95% confidence interval about mean if the sample​ size, n, is 71. How does increasing the sample size affect the margin of​ error, E?

​(c) Construct a 99​% confidence interval about mean if the sample​ size, n, is 33.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?

(d) If the sample size is 15​, what conditions must be satisfied to compute the confidence​ interval?

Answer 1

(d). In order to construct a confidence interval, we are going to make two assumptions:

• The population is normally distributed.
• Each value is sampled independently from each other value.