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Hypothesis Testing of Mean: Cobalamine

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The following information is for Questions 1 through 6.

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 get 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 Pseudo Pharmaceutical (AAP) peddles dietary supplements around the globe.  It is claimed by representatives of AAP 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 AAP 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 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 PseudoPharamaceutical (AAP).

1.  Given the above information, what kind of hypothesis test will you conduct?  Z-test, t-test, &#967;2-test, or F-test?  Please explain.

2.  What will be the null hypothesis, the alternative hypothesis, and, hence, the "tailedness" of the test (left-tailed, right-tailed, or two-tailed)?

3.  What is be the corresponding test statistics?

4.  What is the resultant p-value?

5.  What kind of conclusion can you draw from the hypothesis test you have just performed?  Of course, representatives of AAP 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 AAP?  But, if you are representing MSF, how would you present your argument?  (Hint: Consider a number of confidence levels.)

6.  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 different, what would you do instead?