Statistics for Business: Decision Making and Analysis, 3rd Edition

... to arrive over the next year. Sampling has its own problem: A sample reveals its own proportion of spam, $\widehat{p}$, not the proportion in the population.

The errors in this situation are analogous to those for control charts (Table 14.2). If H₀ is true and the manager retains H₀, then he’s made the right decision. However, the sample proportion $\widehat{p}$ could be small even though H₀ is true. That situation may lead the manager to reject H₀ incorrectly, licensing software that will not be cost effective. That’s the Type I error ✗₁ in Table 16.1. Similarly, it’s possible for the sample to contain a large proportion of spam even if H_a is true. That may cause the office manager to miss an opportunity to reduce costs. That’s the Type II error ✗₂.

Table 16.1 Decisions ...