The recommended daily allowance RDA of cobalamine Vitamin B1

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.
Now, you are asked to weigh in on the dispute between Médecins Sans Frontières (MSF) and
Au & Associates FauxPharamaceutical (FAP)

The tête-à-tête between MSF and FAP broke down, as anyone would have anticipated. They
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 2.85 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

For the sake of argument, let us assume that His Honor, Judge Sushi intends to rule in favor of
MSF. However, he is rather apprehensive of errors in any statistical testing, especially with
respect to Type I and Type II error. Let us assume he picks a 95% significance level to be the
benchmark of this court case

8. 18 Points

A) What is the probability of a Type I error?

B) 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?

C) Plot the corresponding power curve? What do we observed in this plot? Please explain.

Solution