Question

We want to obtain a sample to estimate a population mean. Based on previous evidence, researchers believe the population standard deviation is approximately σ=74. We would like to be 90% confident that the esimate is within 1 of the true population mean. How large of a sample size is required?

n=

Answer 1

Solution :

Given that,

standard deviation = =74

Margin of error = E = 1

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

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

n = ( 1.645 *74 /1 )2

n =14818.19

Sample size = n =14819 ROUNDED