Question

The number of undergraduates at Johns Hopkins University is approximately 2000, while the number at Ohio State University is approximately 40,000. Suppose, instead, that at both schools a simple random sample of about 3% of the undergraduates will be taken. What can we conclude about the sampling variability for the sample proportion from Johns Hopkins as compared to that from Ohio State?

- The sample proportion from Johns Hopkins will have less sampling variability than that from Ohio State.
- The sample proportion from Johns Hopkins will have more sampling variability than that from Ohio State.
- The sample proportion from Johns Hopkins will have about the same sampling variability as that from Ohio State.
- It is impossible to make any statements about the sampling variability of the two samples because the students surveyed were different.

Answer 1

The sample proportion from Johns Hopkins will have more sampling variability than that from Ohio State.

Explanation:

The number of undergraduates at Johns Hopkins University is approximately 2000.

The number at Ohio State University is approximately 40,000.

For John Hopkins:

`n=0.03*2000=60`

For Ohio state:

`n=0.03*40000=1200`

So, the correct answer is :

The sample proportion from Johns Hopkins will have more sampling variability than that from Ohio State.