# Project #88799 - Statistics

My younger brother had a run in earlier with Médecins Sans Frontières.  He narrowly escaped from an adverse verdict by the court........  What he wants is that he be left alone to run his small café.  He asked my oldest brother if he can conduct a survey for him about justice in the Canadian Court.

An initial survey was performed right after Médecins Sans Frontières accused my brother of wrong doing.  Of 1852 customers, 53 were against the aggressive tactics of Médecins Sans Frontières.  After my brother was cleared by the court, a follow-up survey was performed.  Of 4699 customers, 1751 said they did not agree with the aggressive tactics of Médecins Sans Frontières.

1. At the 1% significance level, do the data suggest that a higher percentage of customers were against Médecins Sans Frontières after the court case?

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The recommended daily allowance (RDA) of cobalamine (Vitamin B12) for growing teens is 2.4 μg (micrograms). My brother takes it upon himself to make sure that everyone gets the message. It is generally believed that growing teens are getting less than the RDA of 2.4 μg of cobalamine daily.

It is an open secret that Au & Associates FauxPharmaceutical (FAP) peddles dietary supplements around the globe. It is claimed by representatives of FAP that by taking their vitamin supplement extracted from Atlantic scrod, brand-named as Pillule-au-Sashimi, teens will have the RDA of cobalamine. Médecins Sans Frontières (MSF) has a strong contingent of volunteers in the People's Republic of Banana. It is in this remote republic MSF is going to take on FAP for good.

MSF volunteers managed to collect with a 24-hour period blood samples of 10 randomly selected teens in the People's Republic of Banana for cobalamine. The amounts of cobalamine (in μg) determined in these 10 randomly selected teens are given as follow:

1.85 2.35 1.87 1.90 1.37 2.35 2.55 2.28 1.95 2.49

Based on their global experience, MSF assumes that the population standard deviation of cobalamine in teens to be 0.56 μg.

Médecins Sans Frontières (MSF) and Au & Associates FauxPharamaceutical (FAP) are going to court. To prepare for the upcoming court case, FAP managed to get hold of the same 10 teens randomly selected by MSF, and performed its own testing on them. Their corresponding findings on the teens, in the same order as listed by MSF, are listed below.

2.45 2.8 5 2.87 2.32 1.98 2.51 1.75 1.98 2.03 2.89

It is understandable that FAP would have findings with a higher level of cobalamine in the teens.  But it is important to authenticate FAP's findings. It is imperative to make sure that FAP 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 Au will be offered lifelong supply of bananas from the republic.) After a few tasty bananas, Professor Au 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 FAP group based on a court chosen significance level. Furthermore, Professor Au informed His Honor that it would be unlikely that either MSF or FAP actually knew the population standard deviation at all.

1.    2Perform the statistical test recommended by Professor Au. What significance levels do you think MSF would prefer? On the other hand, what significance levels you think FAP would like to set? Please show work.

2. 3  What if the RDA of cobalamine is actually not well established in the medical community? In fact, it may span a range of values in μg, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6.  What is the corresponding Type II error and power for each of the given assumed RDA value?

 Subject Mathematics Due By (Pacific Time) 10/24/2015 12:00 am
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