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Six STATS Problems Set




Question;The following information is for Questions 1-6.The recommended daily allowance (RDA) of cobalamine (Vitamin B12) for growing teens is 2.4g (micrograms). It is generally believed that growing teens are getting less than the RDA of 2.4g 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 theRDA of cobalamine. FDA is going to take on ntbnPto show that the supplement comes short ofproviding teens with the recommended RDA.FDA managed to collect with a 24-hour period blood sample of 10 randomly selected teensaround the country. The amounts of cobalamine (in g) determined in these 10 randomlyselected teens are given as follow:1.852.351.871.901.372.352.552.281.952.49Based on their national experience, FDA assumes that the the population standard deviationof cobalamine in teens to be 0.56 g.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" ofthe 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 theiradvantage. And so would the officials from FDA. What would you do if you arerepresenting ntbnP? But, if you are representing FDA, how would you present your argument?6. But, wait. What if FDA actually does not know the population standard deviation in thiscase, would you conduct your hypothesis test different? Just in case that you are going toperform the hypothesis different, what would you do instead?7. My brother wants to estimate the proportion of Canadians who own their house. What samplesize should be obtained if he wants the estimate to be within 0.02 with 90% confidence ifa. 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 aform 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. Theproposed cave can only accommodate 36 visitors at one time. In order to give everyone arealistic feeling of the cave experience, the entire length of the cave would be chosen such thatguests 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. Anamusement park consultant proposed a height of the cave based on the 36-guest-at-a-timecapacity. Construction will commence very soon.The park CEO has a second thought at the last minute, and asks yours truly if the proposedheight 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 appropriateheight? Why?9. A virtual bookstore, MBS Direct, routinely, as a matter of business practice, orders lesstextbooks than the amount requested by their registrars office. That is what I have figuredout....... 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 longenough to purchase the required textbook. Let's pick on our STAT 200 students. According tothe 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 staybelow 5% probability of having to back-order from Pearson Custom Publishing? (Note: OurProvost would be very angry when she hears that textbook bundles have to be back-ordered. Inany 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, isthere an approximate method to carry out the analysis in this Quiz #2 question? If so, howwould you do it?10. It is commonly accepted that the mean temperature of human is 98.6oF. Yours truly hasnothing better to do but measured the temperatures of 26 colleagues 1 to 4 times daily to get atotal of 123 measurements. The collected data yielded a sample mean of 98.4oF and a samplestandard deviation of 0.7oF. Is the mean temperature of his colleagues less than 98.6oF at the0.01 significance level? Justify your answer with the proper statistics.11. In this recession, yours truly, CEO of the Outrageous Products Enterprise, would like to makeextra money to support my frequent filet-mignon-and-double-lobster-tail dinner habit. Apromising enterprise is to mass-produce tourmaline wedding rings for brides. Based on mydiligent research, I have found out that women's ring size normally distributed with a mean of6.0, and a standard deviation of 1.0. I am going to order 5000 tourmaline wedding rings frommy 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 sizeshould I order 5000 rings altogether? (Note: It is natural to assume that if your ring size fallsbetween two of the above standard manufacturing size, you will take the bigger of the two.)


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