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 : 27.4 years versus : 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?

Question

14-10-2022
Mathematics

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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 : 27.4 years versus : 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?

Answer :

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Paruljain Paruljain · Answer 1 · 2022-10-26T07:52:25-04:00

No, there is nothing wrong in the research that is done by the head of the institution. He said correct that the mean age of the full time students has declined.

Given above that a university's director of institutional research thought that the average age of full-time students was lowering. The average age of a full-time student in 1995 was 27.4 years old.

He registered all 4934 pupils for this and the average age was 27.1 years.

The fact that the inquiry concerns the average age of a full-time student makes this situation ideal. This is a trustworthy approach when the mean is calculated after accounting for all full-time students at the university.

Given that this is a left-tailed test, the hypothesis is also correct.

He rejected the null hypothesis because p = 0.0020.05.

The average age did decrease, in conclusion. The situation is ideal.

Therefore his hypothesis is absolutely correct. There is nothing wrong with it.

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