Question

Use the given information to find the minimum sample size required to estimate an unknown population mean μ.

How many students must be randomly selected to estimate the mean weekly earnings of students at one college? We want 95% confidence that the sample mean is within $5 of the population mean, and the population standard deviation is known to be $60.

Answer 1

Solution :

Given that,

standard deviation = = 60

margin of error = E = 5

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

Sample size = n = ((Z/2 * ) / E)2

= ((1.960 * 60) / 5)2

= 553

Sample size = 553