In: Statistics and Probability
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.
a
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 ( Using z table )
Sample size = n = (Z/2 / E)2 * * (1 - )
= (1.96 / 0.056)2 * 0.5 * 0.5
= 306.25
Sample size =306
b
Solution
standard deviation = =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* / E] 2
n = ( 1.96*20 / 5 )2
n =61.4656
Sample size = n =62 rounded