Question

How many business students must be randomly selected to estimate the mean monthly earnings of business students at one college? We want 95% confidence that the sample mean is within $131 of the population mean, and the population standard deviation is known to be $529.

Answer 1

Solution First we find the z-score for this Confidance interval: convert 95% to a decimal : 95 loo こ - 1; 0.95 substract from 1: 1 95 ooos Divide by 2. 0:05) 2 0.025 substract from 1-0.025 O: 975 Using a z table We look up this value in the chart; the z-score that goes with this Value is 1-96 Now we use the formula - 2 m Z2/2*6 E 1.96*-529 n = 131 q A-62.644 n=63 The sample size needs to be 63.