Question

To estimate a student’s average score, we need to collect a sample. Assume population standard deviation is equal to 3, If we want to control the error within 0.2 with 98% confidence level, how large the sample size need to be?

Answer 1

Solution :

Given that,

standard deviation =   =3

Margin of error = E = 0.2

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*3 /0.2 )2

n =1217.3

Sample size = n =1218