help with hw **Text for Educational Website:**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 test 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.**- ⓐ 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.- ⓑ 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.- ⓒ Yes, the head of institutional research stated the hypotheses incorrectly; a left-tailed hypothesis test was conducted instead of a two-tailed test.- ⓓ No, the hypothesis test was conducted correctly, and the correct conclusion was made.

The random variable age follows normal distribution. The population mean is 27.4 years. We have to test whether the mean age of full-time students is declined from 27.4 years or not. This is one-sample z-test with left-tailed.The given P-value = 0.0020. There is more chance to reject the null hypothesis and conclude that the mean age of full-time students is declined. But we don’t know the level of significance α. So, we cannot decide without the level of significance. Correct Answer: (A). 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.