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.

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10
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be 111, and the sample standard deviation, s, is found to be 10.
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