The following information is for Questions 1-6

 The following information is for Questions 1-6.

    The recommended daily allowance (RDA) of cobalamine (Vitamin B₁₂) for growing teens is 2.4 µg (micrograms).  It is generally believed that growing teens are getting less than the RDA of 2.4 µg of cobalamine daily.

    A not-to-be-named Pharmaceutical (ntbnP) peddles dietary supplements around the country.  It is claimed by ntbnPrepresentatives that by taking their vitamin supplement, teens will have the RDA of cobalamine.  FDA is going to take on ntbnPto show that the supplement comes short of providing teens with the recommended RDA.

    FDA managed to collect with a 24-hour period blood sample of 10 randomly selected teens around the country.  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 national experience, FDA 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 FDA and ntbnP.

1.  Given the above information, what kind of hypothesis test will you conduct?  Should it be α-test, z-test, t-test, χ²-test, F-test, or Ω-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 corresponding p-value of the hypothesis test?

5.    What kind of conclusion can you draw from the hypothesis test you have just performed?  Of course, representatives of ntbnP would like to have the conclusion skewed to their advantage.  And so would the officials from FDA.  What would you do if you are representing ntbnP?  But, if you are representing FDA, how would you present your argument?

 We can see that the p-value for the test is small. Considering a significance level of 0.05 we are rejecting the null hypothesis as p-value is smaller than the significance level. Thus the data gives sufficient evidence that the claim of ntbnP is false.

6.   But, wait.  What if FDA 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?

7.  My brother wants to estimate the proportion of Canadians who own their house. What sample size should be obtained if he wants the estimate to be within 0.02 with 90% confidence if

a.  he uses an estimate of 0.675 from the Canadian Census Bureau?

b.  he does not use any prior estimates?  But in solving this problem, you are actually using a form of "prior" estimate in the formula used.  In this case, what is your "actual" prior estimate?  Please explain.

8. An amusement park is considering the construction of an artificial cave to attract visitors.  The proposed cave can only accommodate 36 visitors at one time.  In order to give everyone a realistic feeling of the cave experience, the entire length of the cave would be chosen such that guests can barely stand upright for 98% of the all the visitors.

    The mean height of American men is 70 inches with a standard deviation of 2.5 inches.  An amusement park consultant proposed a height of the cave based on the 36-guest-at-a-time capacity. Construction will commence very soon.

    The park CEO has a second thought at the last minute, and asks yours truly if the proposed height is appropriate.  What would be the proposed height of the amusement park consultant?  And do you think that it is a good recommendation?  If not, what should be the appropriate height?  Why?

9. A virtual bookstore, MBS Direct, routinely, as a matter of business practice, orders less textbooks than the amount requested by their registrar’s office.  That is what I have figured out.......  Simply put, MBS Direct has to "eat" the books if they are not sold. 

MBS Direct believes that only 85% of our registered students will stay registered in a class long enough to purchase the required textbook.  Let's pick on our STAT 200 students.  According to the Registrar's Office, we have 600 students enrolled in STAT 200 this spring 2014.

    Suppose you are the CEO of MBS Direct, and you want to perform a probability analysis.  What would be the number of STAT 200 textbook bundles you would order so that you stay below 5% probability of having to back-order from Pearson Custom Publishing?  (Note: Our Provost would be very angry when she hears that textbook bundles have to be back-ordered.  In any case, by next fall, we will no longer need the service of MBS Direct as we are moving 100% to free eResources.  Auf Wiedersehen, MBS Direct......)

    You already know that the exact solution is based on the binomial distribution.  However, is there an approximate method to carry out the analysis in this Quiz #2 question?  If so, how would you do it?

10. It is commonly accepted that the mean temperature of human is 98.6^oF.  Yours truly has nothing better to do but measured the temperatures of 26 colleagues 1 to 4 times daily to get a total of 123 measurements.  The collected data yielded a sample mean of 98.4^oF and a sample standard deviation of 0.7^oF.  Is the mean temperature of his colleagues less than 98.6^oF at the 0.01 significance level?  Justify your answer with the proper statistics.

11. In this recession, yours truly, CEO of the Outrageous Products Enterprise, would like to make extra money to support my frequent filet-mignon-and-double-lobster-tail dinner habit.  A promising enterprise is to mass-produce tourmaline wedding rings for brides.  Based on my diligent research, I have found out that women's ring size normally distributed with a mean of 6.0, and a standard deviation of 1.0.  I am going to order 5000 tourmaline wedding rings from my reliable Siberian source.  They will manufacture ring size from 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, and 9.5.  How many wedding rings should I order for each of the ring size should I order 5000 rings altogether?  (Note: It is natural to assume that if your ring size falls between two of the above standard manufacturing size, you will take the bigger of the two.)