Question: The following information is for Question 7.

The tête-à-tête between MSF and AAP broke down, as anyone would have anticipated. They are going to court.

To prepare for the upcoming court case, AAP managed to get hold of the same 10 teens randomly selected by MSF, and performed their own testing on them. Their corresponding findings on the teens, in the same order as listed by MSF, are listed below.

2.45 2.85 2.87 2.32 1.98 2.51 1.75 1.98 2.03 2.89

It is understandable that AAP would have findings with a higher level of cobalamine in the teens. But it is important to authenticate AAP's findings.

It is imperative to make sure that AAP actually have the same group of teens tested by MSF. His Honor, Judge Ig Sushi is presiding over this landmark case. Unexpectedly, Professor Au is deemed to be able to act impartially, and appointed by His Honor to be the amicus curiæ in this pending court case. (As a reward for his faithful service, Professor Mu will be offered lifelong supply of bananas from the republic.)

After a few tasty bananas, Professor Mu suggested to His Honor that the court should perform a statistical test to see if there is any difference in the means of the MSF group and the AAP group based on a court chosen significance level. Furthermore, Professor Mu informed His Honor that it would be unlikely that either MSF or AAP actually knew the population standard deviation at all.

Perform the statistical test recommended by Professor Mu. What significance levels do you think MSF would prefer? On the other hand, what significance levels you think AAP would like to set?