## STATISTICS 200-The recommended daily allowance (RDA) of cobalamine

STAT 225200STATFall 2015Section 6380Summer 2015Quiz #3Quiz # 3Please answer all 10 questions. The maximum score for each question is posted at thebeginning of the question, and the maximum score for the quiz is 80 points. Make sureyour answers are as complete as possible and show your work/argument. In particular,when there are calculations involved, you should show how you come up with your answerswith necessary tables, if applicable. Answers that come straight from program softwarepackages will not be accepted. The quiz is due by midnight, Sunday, July 5, EasternDaylight Saving Time.IMPORTANT: Per the direction of the Dean’s Office, you are requested to includea brief note at the beginning of your submitted quiz, confirming that your work isyour own.By typing my signature below, I pledge that this is my own work done inaccordance with the UMUC Policy 150.25 – Academic Dishonesty and Plagiarism(http://www.umuc.edu/policies/academicpolicies/aa15025.cfm) on academicdishonesty and plagiarism. I have not received or given any unauthorizedassistance on this assignment/examination._________________________Electronic SignatureYour submitted quiz will be accepted only if you have included thisstatement.Note: In this quiz, you are tested on conceptual understanding of coursematerials. Therefore, you may use program software or calculator program todetermine the mean and standard deviation of any given data set. Also, you mayalso use appropriate free web applets and tables suggested in the StatisticalResources Modules. However, you do need to show how you come up with youranswers. It is important that you show how you come up with the results of yourhypothesis testing, and, explain why you do it certain way, if necessary. No creditwill be extended to just answers without supporting adequate calculations andarguments. Of course, you need only to show the crucial and critical steps as it isdone in the posted homework and quiz solutions.The following information is for Questions 1 through 6.The recommended daily allowance (RDA) of cobalamine (Vitamin B12) for growing teens is2.4 Âµg (micrograms). My brother takes it upon himself to make sure that everyone gets themessage. It is generally believed that growing teens are getting less than the RDA of 2.4 Âµg 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. MÃ©decins Sans FrontiÃ¨res (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 Âµg) determined in these 10 randomly selected teens are given as follow:1.852.351.871.901.372.352.552.281.952.49Based on their global experience, MSF assumes that the population standard deviation ofcobalamine in teens to be 0.56 Âµg.Now, you are asked to weigh in on the dispute between MÃ©decins Sans FrontiÃ¨res (MSF) andAu & Associates FauxPharamaceutical (FAP).1. (3 points) Given the above information, what kind of hypothesis test will you conduct? ztest, t-test, ?-test, ?2-test, Y-test, or F-test? Please explain.2. (3 points) What will be the null hypothesis, the alternative hypothesis, and, hence, the"tailedness" of the test (left-tailed, right-tailed, or two-tailed)?3. (10 points) What is be the corresponding test statistics?4. (5 points) What is the corresponding p-value of the hypothesis test?5. (15 points) What kind of conclusion can you draw from the hypothesis test you have justperformed? Of course, representatives of FAP would like to have the conclusion skewed to theiradvantage. And so would the representatives from MSF. What would you do if you arerepresenting FAP? But, if you are representing MSF, how would you present your argument?6. (10 points) But, wait. What if MSF actually does not know the population standard deviationin this case, would you conduct your hypothesis test different? Just in case that you are going toperform the hypothesis different, what would you do instead?The following information is for Question 7.The tÃªte-Ã -tÃªte 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 teensrandomly selected by MSF, and performed its own testing on them. Their correspondingfindings on the teens, in the same order as listed by MSF, are listed below.2.452.852.872.321.982.511.751.982.032.89It is understandable that FAP would have findings with a higher level of cobalamine in theteens. 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 byMSF. His Honor, Judge Ig Sushi is presiding over this landmark case. Unexpectedly, ProfessorAu is deemed to be able to act impartially, and appointed by His Honor to be the amicus curiÃ¦ inthis pending court case. (As a reward for his faithful service, Professor Au will be offeredlifelong supply of bananas from the republic.)After a few tasty bananas, Professor Au suggested to His Honor that the court should performa statistical test to see if there is any difference in the means of the MSF group and the FAPgroup based on a court chosen significance level. Furthermore, Professor Au informed HisHonor that it would be unlikely that either MSF or FAP actually knew the population standarddeviation at all.7. (16 points) Perform the statistical test recommended by Professor Au. What significancelevels do you think MSF would prefer? On the other hand, what significance levels you thinkFAP would like to set?The following information is for Questions 8 through 10.For the sake of argument, let us assume that His Honor, Judge Sushi intends to rule in favor ofMSF. However, he is rather apprehensive of errors in any statistical testing, especially withrespect to Type I and Type II error. Let us assume he picks a 95% significance level to be thebenchmark 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 medicalcommunity? In fact, it may span a range of values in Âµg, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6. What isthe 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? Pleaseexplain.