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 0.2 irrespective

Answer 1

n is 192

Explanation:

Given data

Cl = 95%

interval = 0.2

to find out

what value n

solution

we have interval = 0.2

so interval has width at most is 0.5 so

margin of error E = 0.2 /2 = 0.1

and we know Z value for 95% Cl is 1.96 from z table

so sample n = Z²/E² ( ( 1 - 0.5) 0.5 + ( 1 - 0.5) 0.5 )

n = 1.96²/0.1² ( ( 1 - 0.5) 0.5 + ( 1 - 0.5) 0.5 )

n = 192.08

so n is 192