The recommended daily allowanceRDAof cobalamineVitamin B12fo

The recommended daily allowance(RDA)of cobalamine(Vitamin B12)for growing teens is2.4 g(micrograms).

My brother takes it upon himself to make sure that everyone getsthemessage. It is generally believed that growing teens are getting less than the RDA of 2.4 g ofcobalamine daily.It is an open secret that Au & Associates FauxPharmaceutical

(FAP) peddles dietarysupplements around the globe.It is claimed by representatives of FAP that by taking theirvitamin supplement extracted from Atlantic scrod, brand-named as Pillule-au-Sashimi,teens willhave the RDA of cobalamine.Médecins Sans Frontières(MSF)has a strong contingent ofvolunteers in the People\'s Republic of Banana.It is in this remote republic MSF is going to takeon FAP for good.MSF volunteers managed to collect with a 24-hour period blood samples of 10 randomlyselected teens in the People\'s Republic of Banana for cobalamine.The amounts of cobalamine(in g)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 g.

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.Theyare 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.

Use the following for 8,9,10

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. (3 points) What is the probability of a Type I error?

9. (10 points) 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 g, 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?

10. (5 points) Plot the corresponding power curve? What do we observed in this plot? Please explain.

Solution

chegg\'s policy allow me to answer 1 question per post

I can gladly help you with your question but you should post it in a new question

8. (3 points) What is the probability of a Type I error?

THE PROBABILITY OF A TYPE I ERROR IS 1 - 0.95 = 0.05