Question

Find the minimum sample size n needed to estimate μ for the given values of​ c, σ​, and E.

c=0.95​, σ=7.5​, and E=11

Assume that a preliminary sample has at least 30 members.

n= ?

​(Round up to the nearest whole​ number.)

Answer 1

Solution

standard deviation =   =7.5

Margin of error = E = 11

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 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* 7.5 /11 )²

n =2

Sample size = n =2