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 109​, and the sample standard​ deviation, s, is found to be 10. ​(a) Construct a 96​% confidence interval about mu if the sample​ size, n, is 29. ​(b) Construct a 96​% confidence interval about mu if the sample​ size, n, is 25. ​(c) Construct a 90​% confidence interval about mu if the sample​ size, n, is 29. ​(d) Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed? LOADING... Click the icon to view the table of areas under the​ t-distribution.

Answer 1

b

Explanation:

Answer 2

a: 105.2 < µ < 112.8

b: 104.872 < µ < 113.128

c: 105.841 < µ < 112.159

d: No, because n < 30

Explanation:

For a - c, see attached photos for work. There are 2 formulas to use. The steps for constructing any confidence interval are the same, you will just use different numbers in the formula depending on what data is given to you.

d: With large sample sizes, the data often resembles normally distributed data, so we can still construct confidence intervals from the data.