Question

How large a sample must be drawn to estimate population proportion confidence interval width to within .04, with 95% confidence, if we believe the true percentage is 80%

Answer 1

Sample size 'n' = 384

Step-by-step explanation:

Step-by-step explanation:-

Given margin of error = 0.04

The sample proportion 'p'= 0.80

The margin of error is determined by

`M.E = (Z_(\alpha ) √(p(1-p)) )/(√(n) )`

`0.04 = (1.96 √(0.80(1-0.80)) )/(√(n) )`

Cross multiplication, we get

`√(n) = (1.96 √(0.80(1-0.80)) )/(0.04 )`

√n = 19.6

Squaring on both sides , we get

n = 384.16≅384