Chapter 7, Problem 5PT

To determine

The correct answer from the option about the best conclusion that (a) the estimate from Johns Hopkins has more sampling variability than that from the Ohio State, (b) the estimate from Johns Hopkins has more sampling variability than that from Ohio State, (c) the two estimates have about the same amount of sampling variability, (d) it is impossible to make any statement about the sampling variability of the two estimates since the students surveyed were different, (e) none of the above.

Answer to Problem 5PT

The correct answer is (b).

Explanation of Solution

Given information:

Number of undergraduates at Johns Hopkins University = 2000

Number of undergraduates at Ohio State University = 40,000

Percent of undergraduates for a sample = 3%

Proportion of students who own an iPod, $p=0.80$

Given that each university has 3% students who own iPod.

Consider that the sample of students from Johns Hopkins University be $n_{\text{JH}}$ and the sample of students from Ohio State University be $n_{\text{OS}}$ .

Since, the number of undergraduates of John Hopkins University is less than the number of undergraduates of Ohio State University; so, $n_{\text{JH}}<n_{\text{OS}}$

Know that if the sample size is larger, then it gives more information about the population and it has less sampling variability. This means, the estimate from Johns Hopkins University has more sampling variability than that from Ohio State.

Hence, the correct answer is (b).