The head of institutional research at a university believed that the mean age of full-time students was declining. In 1995, the mean age of a full-time student was known to be 27.4 years. After looking
at the enrollment records of all 4934 full-time students in the current semester, he found that the mean age was 27.1 years, with a standard deviation of 7.3 years. He conducted a hypothesis of $H_0$:
$\mu = 27.4$ years versus $H_1$: $\mu < 27.4$ years and obtained a P-value of 0.0020. He concluded that the mean age of full-time students did decline. Is there anything wrong with his research?
Choose the correct answer below.
A. Yes, the head of institutional research stated the hypotheses incorrectly, a left-tailed hypothesis test was conducted instead of a two-tailed test
B. Yes, the head of institutional research has access to the entire population, inference is unnecessary. He can say with 100% confidence that the mean age has decreased.
C. Yes, a P-value only indicates the likelihood of getting a result as extreme or more extreme as the one found, the head of institutional research needs to include a confidence level.
D. No, the hypothesis test was conducted correctly, and the correct conclusion was made.
