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

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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?

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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.

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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 ...

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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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