Question

Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 90​% confidence that the sample mean is plus or minus5 IQ points of the true mean. Assume that the standard deviation is 17 and determine the required sample size.

Answer 1

Solution :

Given that,

standard deviation =   =17

Margin of error = E = 5

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645} ( Using z table ( see the 0.05 value in standard normal (z) table corresponding z value is 1.645 )  

sample size = n = [Z_/2* / E] ²

n = ( 1.645 * 17 /5 )²

n =31.2816(rounded)

Sample size = n =31