We judge that introducing better testing can only reduce the rate; therefore, the test is one-sided. From Table I, a critical value of z at a - 0.05 will be -1.645. We note that )~ = nn = 5, so we may use Table VII.

We want the probability of three or fewer cases [P(3 or fewer)], which is 1 - P(4 or more), occurring by chance alone. Using no = 4, P(3 or fewer) = 1 -0.735 = 0.265. There is inadequate evidence to infer an improvement due to the additional screening tests. For illustration, let us calculate the normal approximation, although we know the result will be erroneously different from the Table VII result because of the small )~.

From Eq. (15.13), z -- (Ps - zr) nJn-~ - (0.000200- 0.000333) • ~/15000/0.000333 = -0.893, which is less distant from zero than the critical value; therefore, there is inadequate evidence to infer an improvement. From a statistical software package, p = 0.186.