3 statistics Question

Write the word or phrase that best completes each statement
or answers the question. Express percents as decimals. Round dollar amounts to
the nearest cent.
13. 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.
14. 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?

15. 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 ntbnP representatives that by taking their vitamin
supplement, teens will have the RDA of cobalamine. FDA is going to take on
ntbnP to 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.
a. Given the above information, what kind of hypothesis test will you conduct?
z-test, t-test, ?2-test, F-test, or ?-test? Please explain.
b. What will be the null hypothesis, the alternative hypothesis, and, hence,
the “tailedness” of the test (left-tailed, right-tailed, or
two-tailed)?
c. What is be the corresponding test statistics?
d. What is the corresponding p-value of the hypothesis test?
e. 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?
f. 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?