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).
9. (2 points) Given the above information, what kind of hypothesis test will you conduct? z- test,t-test, Ω-test, χ2-test, Y-test, or F-test? Please explain.
10. (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)?
11. (5 points) What is be the corresponding test statistics?
12. (5 points) What is the corresponding p-value of the hypothesis test?
13. (5 points) What kind of conclusion can you draw from the hypothesis test you have just performed? Of course, representatives of FAP would like to have the conclusion skewed to their advantage. And so would the representatives from MSF. What would you do if you are representing FAP? But, if you are representing MSF, how would you present your argument?
14. (5 points) But, wait. What if MSF actually does not know the population standard deviation in this case, would you conduct your hypothesis test different? Just in case that you are going to perform the hypothesis differently, what would you do instead? Perform the necessary test.