## Transcribed Text

Problem 1
The USDA Women’s Health Survey dataset (nutrient.txt) contains
five types of women’s nutrient intakes which were measured
from a random sample of 737 women aged 25-50 years in United
States. Analyze the dataset according to the following steps:
1. Calculate sample mean and sample standard deviation of
each variable.
2. The recommend intake amount of each nutrient is given in
the following table. For each nutrient, apply a univariate t-test
to test if the population mean of that variable equals the
recommended value. Set the significance level at .
3. Based on the results you obtained in step 2, how would you
interpret your test results? Do you think the US Women meet the
recommended nutrient intake amount? If not, what would you
suggest to the public?
α = 0.05
Variable Calcium Iron Protein Vitamin A Vitamin C
Recommended
Intake Amount
1000mg 15mg 60g 800μg 75mg
Problem 2
The Multiple Testing dataset (multiple.txt) is a simulated
dataset which contains 50 variables and 100 observations per
variable. Suppose we know that the first 10 variables have mean
equal to 2 and the rest of them have mean equal to 0. Analyze
the dataset according to the following steps:
1. Perform multiple testing to the population mean vector to
test if it equals to a vector whose elements are all zeros. Set
the significance level at
2. Based on the test results in step 1, calculate the following
quantities: number of type I errors, FWER and FDP.
3. Redo the multiple testing in step 1 with Bonferroni correction
(set ). Calculate the FWER of your new test results.
4. Redo the multiple testing in step 1 with BH procedure (set
). Calculate the FDP and FWER of your new test results.
How does the results compared with the ones you obtained in
step 1 and step 3?

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