Question

A pilot sample of 75 items was​ taken, and the number of items with the attribute of interest was found to be 30. How many more items must be sampled to construct a 99​% confidence interval estimate for p with a 0.025 margin of​ error?

Answer 1

Answer: 2474

Step-by-step explanation:

Given : A pilot sample of 75 items was​ taken, and the number of items with the attribute of interest was found to be 30.

Then, prior estimate for proportion of attribute of interest: $p=\dfrac{30}{75}=0.4$

Significance level : $\alpha: 1-0.99=0.01$

Critical value : $z_{\alpha/2}=2.576$

Margin of error : $E=0.025$

The formula use to find the sample size :_

$n=p(1-p)(\dfrac{z_{\alph/2}}{E})^2\\\\\Rightarrow\ n=(0.4)(1-0.4)(\dfrac{2.576}{0.025})$

Now, simplify , we get

$n=2548.137984\approx2549$

Now, the number of items more to sample = $2549-75=2474$