Question

A statistics graduate student conducted an experiment about graduate students who lived on campus. After taking a simple random sample of 65 students, she found that twelve students lived on campus. What is the standard error she calculated?
Give your answer to 3 decimal places. For help on how to input a numeric answer, please see "Instructions for inputting a numeric response."

Answer 1

Answer:

She calculated a standard error of 0.048.

Step-by-step explanation:

A proportion p is the number of desired outcomes divided by the number of total outcomes.

The standard error of a proportion is given by:

$SE_{p} = \sqrt{\frac{p(1-p)}{n}}$

In which n is the size of the sample.

In this problem, we have that:

Desired outcomes:

12 students living on campus

Total outcomes:

All the 65 students

Proportion:

$p = \frac{12}{65} = 0.1846$

Standard error of the proportion:

$SE_{p} = \sqrt{\frac{0.1846*0.8154}{65}} = 0.048$