Question

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

How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters? We want 98% confidence that the sample mean is within 3 minutes of the population mean, and the population standard deviation is known to be 8 minutes.

Answer 1

Solution :

Given that,

standard deviation = =8

Margin of error = E = 3

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

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

n = ( 2.326*8 /3 )2

n =38.49

Sample size = n =39 rounded