Question

Using the traditional formula, a 95% CI for p1 − p2 is to be constructed based on equal sample sizes from the two populations. For what value n (= m) will the resulting interval have width at most 0.4 irrespective of the results of the sampling? (Round your answer up to the nearest whole number.) n =

Answer 1

49

Explanation:

Given:

Width = 0.4

Let's take the z value of 95% which is = 1.96

Let's assume population proportion p1 and p2 = 0.5

For margin of error E, the relation between the width and margin of error is 2E.

i.e 2E = 0.4

E = 0.2

To find the sample size, n, let's use the formula :

`n= (z^2*(p_1(1-p_1) + p_2(1-p_2)))/(E^2)`

`= (1.96^2(0.5(1-0.5)+0.5(1-0.5)))/(0.2^2)`

= 48.02

≈ 49