A statistics professor wants to see if more than 80% of her students enjoyed taking her class. At the end of the term, she takes a random sample of students from her large class and asks, in an anonymous survey, if the students enjoyed taking her class. Which set of hypotheses should she test? A) $ \mathrm{H}_{0}: p0.80 $ $ \mathrm{H}_{A}: p=0.80 $ B) $ \mathrm{H}_{0}: p0.80 $ C) $ \mathrm{H}_{0}: p=0.80 $ $ \mathrm{H}_{A}: p0.80 $ D) $ \mathrm{H}_{0}: p

Question

A statistics professor wants to see if more than 80% of her students enjoyed taking her class. At the end of the term, she takes a random sample of students from her large class and asks, in an anonymous survey, if the students enjoyed taking her class. Which set of hypotheses should she test? A) $ \mathrm{H}_{0}: p>0.80 $ $ \mathrm{H}_{A}: p=0.80 $ B) $ \mathrm{H}_{0}: p<0.80 $ $ \mathrm{H}_{A}: p>0.80 $ C) $ \mathrm{H}_{0}: p=0.80 $ $ \mathrm{H}_{A}: p>0.80 $ D) $ \mathrm{H}_{0}: p<0.80 $ $ \mathrm{H}_{A}: p \times 0.80 $ E) $ \mathrm{H}_{0}: p=0.80 $ $ \mathrm{H}_{A}: p<0.80 $

Quizplus · Accepted Answer

The null hypothesis should always be the status quo or the assumption to be tested, and in this case, the assumption is that the proportion of students who enjoyed the professor's class is 80% or greater. Therefore, the null hypothesis should be "p = 0.80" (choice C) and the alternative hypothesis should be "p > 0.80" (choice C) since we want to test if the proportion is more than 80%.

Choices A and B are incorrect because they have the wrong direction of the alternative hypothesis. In choice A, the alternative hypothesis is "p = 0.80," which assumes that the proportion is exactly 80%, but we are interested in testing if it is greater than 80%. Likewise, in choice B, the alternative hypothesis is "p > 0.80," which is the correct direction but the null hypothesis is the opposite of what it should be (it should be "p >= 0.80").

Choice D is incorrect because it has the wrong formulation of the alternative hypothesis. "p x 0.80" is not a valid hypothesis form and does not make sense in this context.

Choice E is also incorrect because it has the wrong direction of the alternative hypothesis. The alternative hypothesis should reflect the research question, which is whether the proportion of students who enjoyed the professor's class is less than 80%, not greater than 80%.

A Statistics Professor Wants to See If More Than 80 H0:p>0.80 \mathrm{H}_{0}: p>0.80 H0​:p>0.80

A Statistics Professor Wants to See If More Than 80 $\mathrm{H}_{0}: p>0.80$