Question

At 95% confidence, how large a sample should be taken to obtain a margin of error of .03 for the estimation of the population proportion? Assume past data are not available for developing a planning value for p*.

Answer 1

The Answer should really be 1,068.

Answer 2

Answer:

The sample should be 1,068.

Step-by-step explanation:

Consider the provided information.

Confidence level is 95% and margin of error is 0.03.

Thus,

1-α=0.95

α=0.05, E=0.03 and planning value $\hat p=0.5$

Formula to calculate sample size is: $n=\frac{\hat p(1-\hat p)(z_{\alpha/2})^2}{E^2}$

From the table we can find:  

$z_{\alpha/2}=z_{0.05/2}\\z_{0.025}=1.96$

Substitute the respective values in the above formula we get:

$n=\frac{0.5(0.5)(1.96)^2}{(0.03)^2}$

$n=\frac{0.25(1.96)^2}{(0.03)^2}\approx 1067.111$

Hence, the sample should be 1,068.