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```Stat 514
Assignment #1
Due 9/2
Statistical Concepts, t-tests, and Randomization
- Montgomery - Chapters 1 and 2
1. You are a lab tech in a doctor’s office. Suppose that there is a test that measures a person’s
cholesterol level but it is not perfect. Numerous testing suggests the test’s uncertainty is described
by a Normal distribution with the mean equal to a patient’s true cholesterol level and a standard
deviation of 8.5 mg/dl. Assuming the doctor considers a cholesterol level above 240 mg/dl to be
a red flag for heart disease, what is the probability that,
a A patient with a true cholesterol level of 225 will be red flagged for heart disease?
b A patient with a true cholesterol level of 250 will not be red flagged for heart disease?
c A patient with a true cholesterol level of 225, using the average of four measurements, will
not be red flagged for heart disease?
d A patient, with a true cholesterol level of 235, takes the test twice (assume independent) and
each test classifies the subject incorrectly?
2. Montgomery 2-20
3. Montgomery 2-24
4. Suppose I generate 10 random variables in the following manner. I first generate a variable X
from a Normal distribution with mean 15 and variance 2. I then randomly generate 10 variables
Y1 , Y2 , ..., Y10 from a Normal with mean 0 and variance 21 and add the variable X to each one.
This creates 10 random variables
Zi = X + Yi
a
b
c
d
What
What
What
What
is
is
is
is
the
the
the
the
i = 1, 2, ...10.
E(Zi )?
Var(Zi )?
E(Z)?
Var(Z)?
5. Montgomery 2-33
6. Montgomery 2-39
7. Montgomery 2-41
8. (SAS/Graph Exercise) Construct a power curve for a two-sided t-test with α = .01, σ = 10 and
n = 12 (total of 24 observations) by calculating the power when δ = 0,2,4,6,8,10,12,14 and 16.
9. Montgomery 2-45
```
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