Question

9) We intend to estimate the average driving time of a group of commuters. From a previous study, we believe that the average time is 42 minutes with a standard deviation of 10 minutes. We want our 99 percent confidence interval to have a margin of error of no more than plus or minus 2 minutes. What is the smallest sample size that we should consider? A) 332 9) B) 166 C) 13 D) 17

Answer 1

Solution :

Given that,

standard deviation = $\sigma$ =10

Margin of error = E = +/-2

At 99% confidence level the z is,

$\alpha$ = 1 - 99%

$\alpha$ = 1 - 0.99 = 0.01

$\alpha$/2 = 0.005

Z_$\alpha$/2 = 2.58 ( Using z table ( see the 0.005 value in standard normal (z) table corresponding z value is 2.58 )  

sample size = n = [Z_$\alpha$/2* $\sigma$ / E] ²

n = ( 2.58* 10/ 2)²

n =166

Sample size = n =166