Final answer:
The correct alternative hypothesis, given the instructor's belief and the data from a sample of 84 students, is p < 0.20. This reflects the hypothesis test aiming to demonstrate that the actual proportion of students who attended is less than 20%.
Step-by-step explanation:
A statistics instructor at Evergreen Valley College believes that fewer than 20% of the students attended the opening night midnight showing of the latest Harry Potter movie. This belief is the basis for conducting a hypothesis test, where the instructor wants to test the claim against a sample of 84 students, out of which 11 attended the movie.
When stating the alternative hypothesis for this one-tailed test, we consider the instructor's belief that the true proportion (p) of attendees is less than 20%. The appropriate alternative hypothesis in this context would be p < 0.20. This suggests that we are looking for evidence to support a proportion that is lower than 20%. The null hypothesis (which is our initial assumption), in this case, would be that the proportion is at least 20% (p ≥ 0.20), and you test against the alternative hypothesis.