Question

Assume that a sample is used to estimate a population mean μ . Find the 99.5% confidence interval for a sample of size 1103 with a mean of 81.5 and a standard deviation of 21.6. Enter your answer as a tri-linear inequality accurate to 3 decimal places.

Answer 1

Given Confidence Interval = 99.5%

Therefore

Given Sample Size = n = 1103

Sample Mean =

Sample Standard Deviation =

STANDARD ERROR:

MARGINAL ERROR:

Therefore the 99.5% Confidence Interval of is

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NOTE: To See the Critical Values of Z; we use the Standard Normal area tabulated values which i posted below.

How to see?

If alpha = 0.5% the confidence interval = 99.5% (Or) Vice Versa

Divide the value 99.5 with 100. you will get 0.995 and after that divide the value 0.995 with 2; you will get 0.4975. Now Search this 0.4975 in side the table ( repeating again see inside the table). You will find this at the intersection of (2.8, 0,01) which is Zcri value i.e 2.81.

Like this you can find the Zcri for any alpha values.