The recommended daily allowance(RDA)of cobalamine

| April 14, 2018

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 ?-test,z-test,t-test,?2-test,F-test, or ?-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 correspondingp-value of the hypothesis test?

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

6. But,
wait. What ifFDA 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 98.6oF. 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
98.4oF and a sample standard deviation of 0.7oF. Is
the mean temperature of his colleagues less than 98.6oF 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 frequentfilet-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.)

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