MATH SOLVE

2 months ago

Q:
# 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?

Accepted Solution

A:

Answer: 2474Step-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: [tex]p=\dfrac{30}{75}=0.4[/tex]Significance level : [tex]\alpha: 1-0.99=0.01[/tex]Critical value : [tex]z_{\alpha/2}=2.576[/tex]Margin of error : [tex]E=0.025[/tex]The formula use to find the sample size :_ [tex]n=p(1-p)(\dfrac{z_{\alph/2}}{E})^2\\\\\Rightarrow\ n=(0.4)(1-0.4)(\dfrac{2.576}{0.025})[/tex]Now, simplify , we get[tex]n=2548.137984\approx2549[/tex]Now, the number of items more to sample = [tex]2549-75=2474[/tex]