Question

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 H0: μ = 27.4 years versus H1: μ < 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?A. No, the hypothesis test was conducted correctly, and the correct conclusion was made.B. 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.C. 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.D. Yes, the head of institutional research stated the hypotheses incorrectly; a left-tailed hypothesis test was conducted instead of a two-tailed test.

Answer 1

A. No, the hypothesis test was conducted correctly, and the correct conclusion was made.

Explanation:

Given that 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.

For this he has recorded all 4934 students and got average as 27.1 years

This is very much perfect because the question is about the mean age of a full time student. when all full time students in the university are taken into account and mean arrived this is a reliable procedure.

The hypothesis also is right as this is left tailed test.

Since p =0.002<0.05 he rejected null hypothesis.

Conclusion is the mean age did decline. Everything is right.

A. No, the hypothesis test was conducted correctly, and the correct conclusion was made.