for a particular population proportion exist and follow a pattern similar to those of the previous two
sections. The main difference is that the only test statistic is z . The logic is based on using a normal
approximation to the binomial as discussed in Chapter 10 .
Notes on the preceding table:
• The standard error for a hypothesis test of a single population proportion is different from that for a
confidence interval for a population proportion. The standard error for a confidence interval,
is a function of , the sample proportion, whereas the standard error for a hypothesis test,is a function of the hypothesized value of p . This is because a test assumes, for the sake of our model,
that p = p 0 . So we use that in the calculation of the standard error. An interval makes no such
assumption.• Like the conditions for the use of a z -interval, we require that the np 0 and n (1 –p 0 ) be large enough
to justify the normal approximation. As with determining the standard error, we use the hypothesized
value of p rather than the sample value. “Large enough” means either np 0 ≥ 5 and n (1 –p 0 ) ≥ 5, or np
0 ≥ 10 and n (1 –p^0 ) ≥ 10 (it varies by text).
example: Consider a screening test for prostate cancer that its maker claims will detect the cancer
in 85% of the men who actually have the disease. One hundred seventy-five men who have been
previously diagnosed with prostate cancer are given the screening test, and 141 of the men are
identified as having the disease. Does this finding provide evidence that the screening test