Selection of Sample Size

Standard error of the sample mean

All else equal, a larger sample size decreases the width of a confidence interval.

[Practice Problems] For a sample size of 65 with a mean of 31 taken from a normally distributed population with a variance of 529, a 99% confidence interval for the population mean will have a lower limit closest to:

A.       23.64.

B.        25.41.

C.        30.09.

[Solutions] A

For a normally distributed population with known variance,

For a 99% confidence interval, use z_0.005 = 2.58.

Therefore, the lower limit = 31-2.58  = 23.6398

[Solutions] B

Sample standard deviation (s) = = 15.670.

For a sample size of 17, degrees of freedom equal 16, so t_0.05 = 1.746.

The confidence interval is 116.23±1.746  = 116.23±6.6357 its width is equal to approximately 13.271.