Question

What sample size would be needed to construct a 95% confidence interval with a 3% margin of error on any population proportion?

Answer 1

SOLUTION:

From given data,

What sample size would be needed to construct a 95% confidence interval with a 3% margin of error on any population proportion

In this problem , we do not have prior information about the proportion.

Let

Confidence level = 95% ,

Desired Margin of Error = E = 3% = 3/100 = 0.03

Note : Margin of Error = (Length of CI) /2

Since we don't have preliminary estimate,

we use   = 0.5 which requires the maximum n

95% confidence interval

Confidence interval is 95%

95% = 95/100 = 0.95

Significance level = = 1 - Confidence interval = 1-0.95 = 0.05

/2 = 0.05 / 2

= 0.025

The Critical Value = Z_/2 = Z_0.025 = 1.96 (From z table)

Sample size

n = (1- ) (Z_/2 / E)²

n = 0.5 (1- 0.5) (1.96 / 0.03)²

n = 0.5 0.5 (65.33333)²

n = 0.5 0.5 4268.4440

n = 1067.111

Since the minimum n has to be integer , we take the ceiling of above number and get n= 1067

Sample Size should be atleast n =1067