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 110​, 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 28. ​(b) Construct an 80​% confidence interval about mu if the sample​ size, n, is 13. ​(c) Construct a 70​% confidence interval about mu if the sample​ size, n, is 28. ​(d) Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed?

Answer 1

(a) Construct an 80​% confidence interval about mu if the sample​size, n, is 28.

107.5173	confidence interval 80.% lower
112.4827	confidence interval 80.% upper
2.48	margin of error

(b) Construct an 80​% confidence interval about mu if the sample​ size, n, is 13.

106.2385	confidence interval 80.% lower
113.7615	confidence interval 80.% upper
3.76	margin of error

(c) Construct a 70​% confidence interval about mu if the sample​ size, n, is 28.

108.0030	confidence interval 70.% lower
111.9970	confidence interval 70.% upper
2.00	margin of error

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

We could not have computed the confidence intervals in parts (a) - (c) if the population had not been normally distributed since for applying t distribution, the population must be a normal distribution.