To collect data in an introductory statistics course, recently I gave the students a questionnaire. One question asked whether the student was a vegetarian. Of 25 students, 0 answered "yes." They were not a random sample, but let us use these data to illustrate inference for a proportion. Let π denote the population proportion who would say "yes."
Consider H₀: π = 0.50 and Hₐ: π ≠ 0.50.

a. What happens when you try to conduct the "Wald test," for which z = (p - π₀)/√p(1 - p)/n] uses the estimated standard error?
b. Find the 95% "Wald confidence interval" (1.3) for π. Is it believable? (When the observation falls at the boundary of the sample space, often Wald methods do not provide sensible answers.)