Question

The number of undergraduates at Johns Hopkins University is approximately 2000, while the number at Ohio State University is approximately 40,000. A simple random sample of 50 undergraduates at Johns Hopkins University will be obtained to estimate the proportion of all Johns Hopkins students who feel that drinking is a problem among college students. A simple random sample of 50 undergraduates at Ohio State University will be obtained to estimate the proportion of all Ohio State students who feel that drinking is a problem among college students. Answer Questions 4-5 below.

Answer 1

The remaining part of Question:

4) what can we conclude about sampling variability in the sample proportion calculated in the sample at John Hopkins as compared to that calculated in the sample at Ohio State.

5) The number of undergraduates at Johns Hopkins is approximately 2000 while the number at Ohio State is approximately 40000, suppose instead that at both schools, a simple random sample of about 3% of the undergraduates Will be taken.

Answer:

4) The sample proportion from Johns Hopkins will have about the same sampling variability as that from Ohio State

5) The sample proportion from John Hopkins will have more sampling variability than that from Ohio State

Step-by-step explanation:

Note: The sampling variability in the sample proportion decreases with increase in the sample size.

4) since the sample size at both Johns Hopkins and Ohio State is the same (i.e. n = 50), the sample variability of the sample proportion will be the same for both cases.

5) 3% of the population are selected for the observation in both cases.

At Johns Hopkins, sample size, n = 3% * 2000

n = 60

At Ohio State, sample size, n = 3% * 40000

n = 1200

Since sampling variability in the sample proportion decreases with increase in the sample size, the sampling variability in sample proportion will be higher at Johns Hopkins than at Ohio State.