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.

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\ (1)/(√(n))`

Also, by equation of inverse variation , we have

`E_1√(n_1)=E_2√(n_2)`

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

`20√(45)=5√(n_2)\\\\\Rightarrow\ √(n_2)=4√(45)`

Taking square on both sides , we get

`n_2=(4√(45))^2=4^2*45=720`

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