Question

For a 95% confidence interval what would the sample size need to be as it's most conservative to have a 2% margin of error

Answer 1

The size of the sample 'n' = 2401

Explanation:

Step:1

Given that the margin of error = 2 % = 0.02

The margin of error is determined by

`M.E = (Z_(0.05) √(p(1-p)) )/(√(n) )`

we know that the proportion

`√(p(1-p)) < (1)/(2)`

Step:2

The margin of error is determined by

`0.02 = (1.96( (1)/(2) ) )/(√(n) )`

`√(n) = (1.96)/(2 X 0.02)`

√n = 49

Squaring on both sides, we get

n = 49 × 49

n = 2401

Final answer:-

The size of the sample 'n' = 2401