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Statistics: Conclusions for Cobalamine (vitamin B12) in Growing Teens

The recommended daily allowance (RDA) of cobalamine (vitamin B12) for growing teens is 2.4ug (micrograms). It is generally believed that growing teens are getting less than the RDA of 2.4ug of cobalamine daily. The FDA managed to collect with a 24-hour period blood samples of 10 randomly selected teens around the country. The amounts of cobalamine (in ug) determined in these 10 randomly selected teens are given as follows:

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, the FDA assumes that the population standard deviation of cobalamine in teens to be 0.56ug. Now, you are asked to weigh in on the dispute between the FDA and ntbnP.

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

Solution Preview

We can conduct a z-test, as the population standard deviation of cobalamine in teens to be 0.56ug. The two hypotheses are:

Null hypothesis H0: mu >= 2.4 ug
Alternative hypothesis Ha: mu < 2.4 ug

Here mu is the average RDA of cobalamine (vitamin B12).

We can find the sample mean as ...

Solution Summary

In about 200 words, this solution addresses this scenario using a z-test and shows how to conduct a hypothesis test and make a conclusion regarding the given results. All calculations are provided. Additionally, comments on how to skew the data are also included.