The article “Repeatability and Reproducibility for Pass/Fail Data” (J. Testing Eval. 1997: 151–153) reported that in n = 48 trials in a particular laboratory, 16 resulted in ignition of a particular type of substrate by a lighted cigarette. Let p denote the long-run proportion of all such trials that would result in ignition.

a. Use the score interval (8.15) to construct a 95% CI for p.

b. Use the Wald interval (8.16) to construct a 95% CI for p.

c. How do the intervals in parts (a) and (b) compare? Is the narrower interval preferable here? Why or why not?

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√p(1-P)/n+2/2/4n² p±za/27 1+2/2/n where p = [p+2/2/2n]/[1+2/2/n]. This is often referred to as the score CI for p.