Question

Determine the sample size needed to obtain an estimate of µ if the margin of error E = 0.06, σ = 0.75, and the confidence level is 99%

a) Find α for 99% confidence level.

α =

(b) Find 1 − α/2.

1 − α/2 =


(c) Find z_α/2 for a 99% confidence level.

z_α/2 =

Answer 1

Solution :

Given that,

standard deviation =   =0.75

Margin of error = E = 0.06

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.576

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

n = ( 2.576*0.75 / 0.06 )2

n =1036.84

Sample size = n =1037