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

Answer:

Sample size 'n' = 384

Step-by-step explanation:

Explanation:-

Given margin of error = 0.04

The sample proportion 'p'= 0.80

The margin of error is determined by

                               $M.E = \frac{Z_{\alpha } \sqrt{p(1-p)} }{\sqrt{n} }$

                             $0.04 = \frac{1.96 \sqrt{0.80(1-0.80)} }{\sqrt{n} }$

Cross multiplication, we get

                             $\sqrt{n} = \frac{1.96 \sqrt{0.80(1-0.80)} }{0.04 }$

                             √n = 19.6

Squaring on both sides , we get

                            n = 384.16≅384