Question

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, is found to be 109, and the sample standard​ deviation, s, is found to be

10.

​(a) Construct a 98% confidence interval about m μ if the sample​ size, n, is 21.

​(b) Construct a 98% confidence interval about mu μ if the sample​ size, n, is 26.

​(c) Construct a 99% confidence interval about mu μ if the sample​ size, n, is 21.

​(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 = 103.4835
Upper Limit =
Upper Limit = 114.5165
98% Confidence interval is ( 103.4835 , 114.5165 )

Part b)

Confidence Interval



Lower Limit =
Lower Limit = 104.1263
Upper Limit =
Upper Limit = 113.8737
98% Confidence interval is ( 104.1263 , 113.8737 )

Part c)

Confidence Interval



Lower Limit =
Lower Limit = 102.791
Upper Limit =
Upper Limit = 115.209
99% Confidence interval is ( 102.791 , 115.209 )

Part D)

No, it is not possible to draw confidence interval if the population is not normal.