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A sports reporter randomly surveyed 53 football linemen from large universities (enrollment $> 10{,}000$) and randomly surveyed $53$ football linemen from smaller colleges (enrollment $< 10{,}000$ ).

Suppose the researcher wished to test whether linemen from large universities are heavier than linemen from smaller colleges. He finds that the average weight of linemen at large universities is $287\text{ lbs}$, while the average weight of linemen at small colleges is $268\text{ lbs}$.

Which of the following statements is true?

A

A matched pairs $T$ procedure would be appropriate, where linemen from the smaller school could be appropriately paired with lineman from the larger school.

B

A weight difference of at least $9.8\text{ lbs}$ would be needed to be able to successfully claim players from the large university weigh more at the alpha = $5\%$ level.

C

Assumptions are not met in this situation for any inferential procedure to be carried out.

D

If $100$ more random university and college linemen were surveyed, and respective means of µ(college) = $268$ and µ(universities) = $287$ were found, then the P-value and test statistic would most likely remain the same.

E

A smaller standard deviation in both samples’ weights will give stronger evidence that university linemen weigh more.

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