Math 143 C/E, Spring 2001
IPS Reading Questions
Chapter 8, Section 1, Part 2: pp. 588-595



  1. In the description of the “Large-Sample Significance Test for a Population Proportion” (see p. 589), the denominator for the z statistic uses the value p0 proposed in the null hypothesis instead of the standard error of . Why is this?

    Remember that the goal of a hypothesis test is different from that of a confidence interval. Specifically, we are testing the compatability of our sample proportion against a proposed value p0 for the population proportion. The only reason we resorted to using the standard error of in the first place was because we didn't know the population proportion (and hence we didn't know s). But in a significance test we deal in hypotheticals; in particular, we propose that the population proportion be p0. If we're going to propose it, then we should go all the way in our assumption, which means that, if it were the correct parameter, then s is what appears in the denominator.

  2. If you want the margin of error for a 95% confidence interval for a population proportion to be less than 0.01, what sample size should you use at a minimum? Would your answer change if you knew that the population proportion was no bigger than 0.25?

    If you have no knowledge of the value of p, the population proportion, then a safe sample size would be


    n = (1.96/0.02)2 = 9604.
    If, on the other hand, you knew that p £ 0.25, then you could use a sample size as small as


    n = (0.25)(0.75)(1.96/0.01)2 = 7203.