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 115​, and the sample standard​ deviation, s, is found to be 10. ​(a) Construct a 98​% confidence interval about mu if the sample​ size, n, is 16. ​(b) Construct a 98​% confidence interval about mu if the sample​ size, n, is 20. ​(c) Construct a 99​% confidence interval about mu if the sample​ size, n, is 16. ​(d) Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed?

Answer 1

Part a)

Confidence Interval



Lower Limit =
Lower Limit = 108.4938
Upper Limit =
Upper Limit = 121.5062
98% Confidence interval is ( 108.4938 , 121.5062 )

Part b) n = 20

Confidence Interval



Lower Limit =
Lower Limit = 109.3215
Upper Limit =
Upper Limit = 120.6785
98% Confidence interval is ( 109.3215 , 120.6785 )

Part c) n = 16

Confidence Interval



Lower Limit =
Lower Limit = 107.6332
Upper Limit =
Upper Limit = 122.3668
99% Confidence interval is ( 107.6332 , 122.3668 )

Part d)

No, because the requirement for calculating a t interval for sample size less than 30 the data should come from a population that is normally distributed.