Question

1. Find an estimate of the sample size for the following questions.

a. A population proportion is to be estimated. Estimate the minimum sample size needed to achieve a margin of error of E = 0.056 with a 95% degree of confidence.

b. A population mean is to be estimated. Estimate the sample size needed to obtain a margin of error of E = 5 and standard deviation = 20 with 95% degree of confidence.

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.056

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.96 / 0.056)2 * 0.5 * 0.5

= 306.25

Sample size =307

(B)

Solution

standard deviation =  σ =20

Margin of error = E = 5

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

sample size = n = [Z/2* σ / E] 2

n = ( 1.96*20 /5 )2

n =61.4656

Sample size = n =62