Question

We would like to estimate teacher's salaries in the Baltimore County school district. How many teachers must be randomly select so that we have can have 95% confidence that our estimate is within $2,000 of the true population mean (Assume that the population standard deviation is $6,000)?

		6
		34
		35
		43

Answer 1

:

Solution

standard deviation =s =   =6000

Margin of error = E = 2000

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )

sample size = n = [Z/2* / E] 2

n = ( 1.96* 6000/ 2000 )2

n =35

Sample size = n =35