Statistics 2MA3 Assignment #2

Statistics 2MA3 - Assignment #2

2003-02-11

Due: 2003-03-03 18:00

The numbered problems are from Rosner, Fundamentals of Biostatistics, 5th Edition. Most of the problems can be solved on your calculator, some will also require statistical tables. Wherever possible, use R to check you answers and submit your R code with your solutions.

Chapter 4

A. Hypertension (p. 110) 4.36-4.38 - see the hint.

B. Cardiovascular Disease (p. 114) 4.78-4.80

C. Endocrinology (p. 115) 4.89-4.90 - see the hint.

Chapter 5

D. Pulmonary Disease (p. 148) 5.31-5.34

E. Pulmonary Disease (p. 150) 5.53-5.55

F. Variance of a Linear Combination of Random Variables

Suppose that n = 9 observations X₁, ..., X₉ each have the same variance s² but are autocorrelated, with

Corr(X_i, X_j) = r_ij = r^{|j - i|}

for some 0 < r < 1. Apply Equation 5.13 on page 138 to find the standard error of the sample mean. Show that the standard error increases from s /sqrt(n) to s as r increases from 0 to 1. What is the importance of this result for measurements replicated under laboratory conditions?

G. Linear Combinations of Random Variables (and a few other things)

Suppose that apples from a certain orchard have a mean weight of 90 g with a 10% coefficient of variation. If they are packed 12 to a bag, what is the probability that the bag will weigh less than 1 kg? Given 100 bags, what is the probability that at least 1 will weigh less than 1 kg? Given 1000 bags, what is the probability that at least 10 will weigh less than 1 kg? State any assumptions you make.