If we wanted to create a new 90% confidence interval from a different sample for the proportion of those with a two on one date while keeping the margin of error at 0.05, what w…

Question

asked Jan 25, 2020 67.8k views

1 Answer

Pedram Shabani · Answer 1 · 2020-01-31T20:22:09+0000

Answer: 271

Explanation:

The formula we use to find the sample size is given by :-

$n=p(1-p)((z_(\alpha/2))/(E))^2$

, where
$z_(\alpha/2)$ is the two-tailed z-value for significance level of
$(\alpha)$

p = prior estimation of the proportion

E = Margin of error.

If prior estimation of the proportion is unknown, then we take p= 0.5 , the formula becomes

$n=0.5(1-0.5)((z_(\alpha/2))/(E))^2$

$n=0.25((z_(\alpha/2))/(E))^2$

Given : Margin of error : E= 0.05

Confidence level = 90%

Significance level
$\alpha=1-0.90=0.10$

Using z-value table , Two-tailed z-value for significance level of
0.10

$z_(\alpha/2)=1.645$

Then, the required sample size would be :

n=0.25((1.645)/(0.05))^2

Simplify,

$n=270.6025\approx271$

Hence, the required minimum sample size =271