Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Transcript

Stat 514 Assignment #1 Due 9/2 Statistical Concepts, t-tests, and Randomization - Montgomery - Chapters 1 and 2 READING 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