Question

In a 2003 report based on the data from the National Health and Nutrition Examina- tion Survey (NHANES) conducted annually in the US, investigators included the following summary values (in mg) of daily iron intake for the 20-39 age group:

Female - Mean = 13.7 Median = 11.7 Standard Deviation = 8.9

Male - Mean = 17.9 Median = 15.7 Standard Deviation = 10.9

1. (i) Based on these summary measures, does it make sense to assume that daily iron intake levels for males and females in the 20-39 age group are Normally distributed? Explain briefly.

2. (ii) Suppose that we plan to observe the mean daily iron intake for 100 randomly selected females aged between 20 and 39 years. What is the distribution of this mean? What are the values of its mean and standard deviation? Justify your answer briefly.

3. (iii) We plan to observe the mean daily iron intake for 100 randomly selected men aged between 20 and 39 years. Use MINITAB to find the probability that their mean daily iron intake is below the RDA for men in that age group of 8 mg. If you are using Normal distribution for this calculation, clearly state what quantity is assumed to be Normal and why. Also include values of the mean and standard deviation for this distribution.

2. (b) Here is another report in which the iron intakes, in milligrams, were obtained during a 24-hour period for 45 randomly selected adult females under the age of 39.
   You will need the MINITAB worksheet called Iron.MTW which you can download from the Data files folder -¿ Practicals -¿ Resouces within the Moodle to answer the questions that follow.

   1. (i) Calculate and interpret the 95% confidence interval for the population mean based on 24 hour iron intake. All calculations should be done manually without using Minitab.

   2. (ii) Perform an appropriate hypothesis test to determine whether the mean iron intake of women under the age of 39 is different to the RDA of 18 mg. Test at 1% significance level. You should use the 5-step process Graph-State-Formulate-Solve and Conclude.

   3. (iii) Using your MINITAB output from part (ii), give and interpret the 99% confidence interval for the population mean iron intake of women under the age of 39.

3. (c) Based on your results from the previous parts, are men and women under the 39 age group getting enough iron through their diet? Explain briefly.

Answer 1

1. Since the mean and median are almost coincides, we can assume that the distribution is normal

2. The distribution of the mean follows Normal distribution with mean $\bar X$ and standard deviation $\sigma / \sqrt{n}$

Replacing the values we can say the distribution will follow

3. For male sample of 100, it follows Normal distribution with mean $\bar X$ and standard deviation $\sigma / \sqrt{n}$

Replacing the values we can say the distribution will follow

$P(X<8) = P(\frac{X-17.9}{1.09} < \frac{8-17.9}{1.09}) = P(Z<-8.33) = 0$

** The data file is missing for the other questions **