Question

A researcher conducted a study of the access speed of 45 hard drives and concluded that his maximum error of estimate was 20. if he were to conduct a second study to reduce the maximum error of estimate to 5, about how many hard drives should he include in his new sample?

Answer 1

Answer: He should include 720 hard drives in his new sample.

Step-by-step explanation:

• Margin of error is inversely proportional to the square root of the sample size.

Let E be the margin of error and n be the sample size , then 4

$E\ \alpha\ \dfrac{1}{\sqrt{n}}$

Also, by equation of inverse variation , we have

$E_1\sqrt{n_1}=E_2\sqrt{n_2}$

Put $n_1=45,\ E_1=20 , E_2=5$  (given) , we get

$20\sqrt{45}=5\sqrt{n_2}\\\\\Rightarrow\ \sqrt{n_2}=4\sqrt{45}$

Taking square on both sides , we get

$n_2=(4\sqrt{45})^2=4^2\times45=720$

Hence, he should include 720 hard drives in his new sample.