Exercise 10. Sample size

So far we have said that the difference between the proportion of Democratic voters and Republican voters is about 10% and that the standard error of this spread is about 0.2 when \(N=25\). Select the statement that explains why this sample size is sufficient or not.

Possible answers

This sample size is sufficient because the expected value of our estimate \(2\bar{X}-1\) is \(d\) so our prediction will be right on.

This sample size is too small because the standard error is larger than the spread.

This sample size is sufficient because the standard error of about 0.2 is much smaller than the spread of 10%.

Without knowing p, we have no way of knowing that increasing our sample size would actually improve our standard error.