Question

How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters?...

How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters? We want 95% confidence that the sample mean is within 3 minutes of the population mean, and the population standard deviation is known to be 12 minutes

Homework Answers

Answer #1

Solution :

Given that,

standard deviation =   =12

Margin of error = E = 3

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* 12 / 3 )2

n =61.4656(rounded)

Sample size = n =62

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