Question

A principal of a large high school wants to estimate the true proportion of high school students who use the community's public library. To do so, he selects a random sample of 50 students and asks them if they use the community's public library. The 95% confidence interval for the true proportion of all students who use the community's public library is 0.25 to 0.34. If the principal had used a sample size of 200 students rather than 50 students, how would the length of the second interval compare to the original interval?
O It would be half as wide.
O It would be twice as wide.
O It would be one-fourth as wide.
O It would be four times as wide
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Answer 1

Considering the margin of error of a confidence interval, it is found that the correct option is:

It would be half as wide.

What is the margin of error of a confidence interval?

It is modeled by:

$M = z\frac{s}{\sqrt{n}}$

In which:

• z is the critical value.

• s is the standard deviation.

• n is the sample size.

From this, we get that the margin of error is inversely proportional to the square root of the sample size. Then, multiplying the sample size by 4, when it changes from 50 to 200, cuts the margin of error in half, making the interval half as wide.

More can be learned about the margin of error of a confidence interval at brainly.com/question/25890103