must show all the work no plagisrism.

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). It is generally believed that growing teens are getting less than the RDA of

2.4 µg of cobalamine daily.

Médecins Sans Frontières (MSF) volunteers managed to collect a within 24-hour-period blood sample of 10 randomly selected teens in a developing 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 global experience, MSF assumes that the population standard deviation of cobalamine in teens to be 0.56 µg.

You are to determine if these teens are getting the recommended daily allowance of cobalamine. The host country may dispute the finding.

1. (3 points) Given the above information, what kind of hypothesis test will you conduct? z- test, t-test, Ω-test, χ2-test, Y-test, or F-test? Please explain.

2. (3 points) What will be the null hypothesis, the alternative hypothesis, and, hence, the "tailedness" of the test (left-tailed, right-tailed, or two-tailed)?

3. (10 points) Perform the hypothesis test. What is the resulting test statistics?

4. (5 points) What is the corresponding p-value of the hypothesis test?

5. (15 points) What kind of conclusion can you draw from the hypothesis test you have just performed? Of course, the host country may not like the finding. On the other hand, representatives from MSF may want to defend theirs. What would you do if you are representing the host country? But, if you are representing MSF, how would you present your argument?

6. (10 points) 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 differently, perform this alternative test.

The following information is for Question 7.

The tête-à-tête between MSF and the host country broke down, as anyone would have anticipated. They are going to a third party for mediation.

To prepare for the upcoming mediation process, the host country managed to get hold of the same 10 teens randomly selected by MSF, and performed its own testing on them. Their corresponding findings on the teens, in the same order as listed by MSF, are listed below.

2.45 2.85 2.87 2.32 1.98 2.51 1.75 1.98 2.03 2.89

It is understandable that the host country would have findings with a higher level of cobalamine in the teens. But it is important to authenticate its findings.

It is imperative to make sure that the host country actually has the same group of teens tested by MSF. As it has been verified, the mediator suggested that a statistical test should be performed to see if there is any difference in the means of the MSF group and the later testing group based on a chosen significance level. Furthermore, the mediator considered that it would be unlikely that either MSF or the host country actually knew the population standard deviation at all.

7. (16 points) Perform the statistical test recommended by the mediator. What significance levels do you think MSF would prefer? On the other hand, what significance levels you think the host country would like to set?

The following information is for Questions 8 through 10.

For the sake of argument, let us assume that the mediator intends to rule in favor of

MSF. However, he is rather apprehensive of errors in any statistical testing, especially with respect to Type I and Type II error. Let us assume he picks a 95% significance level to be the benchmark of this mediation case.

8. (3 points) What is the probability of a Type I error?

9. (10 points) What if the RDA of cobalamine is actually not well established in the medical community? In fact, it may span a range of values in µg, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6. What is the corresponding Type II error and power for each of the given assumed RDA value?

10. (5 points) Plot the corresponding power curve? What do we observed in this plot? Please explain.

(For Questions 11 &12) UMUC Stats Club conducted an online poll of 500 adults in May 2017. One question was “Do you believe that the climate change is due to global warming?”. Out of the 500 adults, 420 adults answered “Yes”.

11. (4 pts) Find a 90% confidence interval estimate of population proportion of adults who support the claim that climate change is due to global warming. (Explain how you get the critical value, show work and round the answer to three decimal places)

12. (10 pts) In a similar online poll conducted in 2016, 80% of adults supported the claim. In order to determine if the proportion of adults who support the claim in 2017 is higher than one year ago, we would like to perform the following hypothesis test:

(a) (4 pts) Find the test statistic. (Show work and round the answer to two decimal places)

(b) (4 pts) Determine the P-value for this test. (Show work and round the answer to three decimal places. If you use technology to find the P-value, you have to describe the steps)

(c) (2 pts) Is there sufficient evidence to justify the rejection of at the α=0.05 level? Explain.