BIOLOGY 446
HOMEWORK 2
1a. Many statistical procedures require us to consider SUMS, DIFFERENCES and AVERAGES
of random variables. On this and the next two homework sheets we will therefore consider
examples of these in the simple context of rolling a fair
BIOLOGY 446
HOMEWORK 12
Paired two-sample t tests
1. A physiologist claims that, on physiological grounds, men should have a higher
mean blood pressure than women. We wish to test this theory. Formulate a
BIOLOGY 446
HOMEWORK 11
Note: In all questions in this homework, you may assume that the data are realized values
of random variables having normal distributions. However, in none of these questions are
the variances of these distributions known.
Instruct
BIOLOGY 446
HOMEWORK 9
1. In class you were given two formulae for the z score that compares two binomial probability
estimates. These were given in the notation where the contingency table entries are:
Col 1
Col 2
Total
Row 1
Row 2
o11
o21
o12
o22
r1
r2
BIOLOGY 446
HOMEWORK 10
1. Suppose that the observed value of the chi-square statistic in a 2 x 2 table is 4.41. Can you find
the P-value corresponding to this value using only the chi-square chart of cut-off points handed out
in class? Can you place boun
BIOLOGY 446
HOMEWORK 5
1. Suppose that we know that the height of a woman chosen at random is a random variable
coming from a normal distribution with mean 66, variance 9. (Height is measured in inches.)
Find
(a) the probability that the height of a woman
BIOLOGY 446
HOMEWORK 4
The die or dice referred to in this homework are all fair tetrahedral (i.e. four sided) dice.
Please assume the dice are four-sided (NOT six-sided).
This (long) homework is worth 40 points, i.e. twice as many as previous homework.
1
BIOLOGY 446
HOMEWORK 3
1. In last week's homework, you found (in question 1) the probability distribution of T2, where T2
is the sum of the numbers turning up on two rolls of a fair six-sided die. You also found the
probability distribution for D, the dif
BIOLOGY 446
HOMEWORK 7
INTRODUCTION TO HYPOTHESIS TESTING
Questions 1 - 3 in this homework give an informal introduction to problems of hypothesis
testing in the simple context of coin tossing. Questions 4 and 5 are a preparation for hypothesis
testing pr
BIOLOGY 446
HOMEWORK 6
1. A medical researcher interested in the genetic basis of chronic bronchitis collects data from 1000
single-child families where both parents suffer from this illness (so that n = 1000). She finds that
375 of the children also suff
BIOLOGY
446
HOMEWORK 8
1. We wish to test the null hypothesis that a certain coin is fair. The alternative hypothesis is that
the coin is unfair. (That is, the alternative hypothesis is two-sided.) A Type I error of 1% is
chosen. Suppose that we plan to t
BIOLOGY 446
HOMEWORK 12
Paired two-sample t tests
1. A physiologist claims that, on physiological grounds, men should have a higher
mean blood pressure than women. We wish to test this theory. Formulate a