Discussion
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 of the following set of hypotheses should she set ?
Answer: C
She should test H0 : p = 0.80 against H1 : p > 0.80.
The claim she wants evidence for, that more than 80% enjoyed the class, goes in the alternative hypothesis, and the null states the boundary value of no effect, p = 0.80. Rejecting the null then supports the claim.
\(p \lt 0.80\) tests the opposite direction, and \(p \neq 0.80\) is two-sided although only one direction interests her. Putting the claim \(p \gt 0.80\) in the null, with an equality alternative, reverses the roles of the hypotheses.
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