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A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 attended the midnight showing. An appropriate alternative hypothesis is:

a) p > 0.20
b) p = 0.20
c) p < 0.20
d) p ≠ 0.20

User Dorsey
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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.

User Tauren
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