Question

For a random sample of 16 recent business school graduates beginning their first job, the mean starting salary was found to be $39,500, and the sample standard deviation was $8,500. Assuming the population is normally distributed, calculate the lower confidence limit (LCL) of the population mean with a 0.05.

Answer 1

Given, n = 16 ,sample mean (x bar) = 39500

Standard deviation (s) = 8500

Alpha = 0.05

Then Z* = z score at alpha = 0.05 level.

Which is Z* = 1.645

Then Lower confidence limit is given by

$X bar - Z^{*}\frac{s}{\sqrt{n}}$

= 39500 - 1.645×8500/√16

= 36004.375

So the lower confidence limit of the population mean with alpha= 0.05 is $36004.375