A simple random sample of size n is drawn The sample mean x

A simple random sample of size n is drawn. The sample mean, x, is found to be 17.9, and the sample standard deviation, s, is found to be 4.8.

A) Construct a 95% confidence interval about u if the sample size, n is 35.

The confidence interval is (ascending order)

B) Construct a 95% confidence interval about u if the ssample size, n, is 61.

The confidence interval is (ascending order)

C) Construct a 99% confidence interval about u if the sample size, n is 35

The confidence interval is (ascending order)

(A) Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So the lower bound is

xbar - Z*s/vn =17.9 - 1.96*4.8/sqrt(35) =16.30976

So the upper bound is

xbar + Z*s/vn =17.9 + 1.96*4.8/sqrt(35) =19.49024

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(b)

So the lower bound is

xbar - Z*s/vn =17.9 - 1.96*4.8/sqrt(61) =16.69543

So the upper bound is

xbar + Z*s/vn =17.9 + 1.96*4.8/sqrt(61) =19.10457

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(c)Given a=1-0.99=0.01, Z(0.005) = 2.58 (from standard normal table)

So the lower bound is

xbar - Z*s/vn =17.9 - 2.58*4.8/sqrt(35) =15.80672

So the upper bound is

xbar + Z*s/vn =17.9 + 2.58*4.8/sqrt(35) =19.99328