STA 6208 – Spring 2013 – Homework 1
Due – Friday 1/22/16
Part 1: Oehlert: Chapter 2: 1,4,5 (For each, use a normal t-test and randomization test)
Part 2: A paired difference experiment is to be conducted to compare 2 treatments (paired implies that each
subject receives each treatment). The data are generated by the following structure:
Yij  i   j   ij
i  1,2

j  1,..., n  j ~ NID 0,  2

p.2.a. Derive the distributions of D j  Y1 j  Y2 j and D 
 ij ~ NID0, 2   i    ij 
1 n
 Dj
n j 1
p.2.b. Derive the formula for obtaining the sample size needed (number of paired observations) to detect a
difference of with power = 1-Typeerror rate of when we test H0: versus HA:
≠ with a Type I error rate of . Note that we will be using the following test statistic, but we use the
large-sample z-approximation to obtain sample size:
 D
n
t obs 
D
SD
H0
n
~
t n1
where
SD 
j 1
j
D

2
n 1
p.2.c. Based on your result from p.2.b., complete the following table.

.05
.05
.05
.05
.01
.05
.01

.20
.20
.20
.20
.20
.10
.10

10
4
4
4
10
10
10

3
6
3
6
3
3
3
n
Part 3: Jack conducts an independent sample t-test to compare 2 treatments, based on n1 = n2 = 12 subjects per
treatment. Jill conducts a paired sample t-test with n=8 subjects.
Jack’s degrees of freedom for error (based on the pooled variance) = ___________________
Jill’s degrees of freedom for error (based on the paired difference variance) = _______________
Suppose Jack’s estimate of experimental error variance is 125, and Jill’s is 25. Give the relative efficiency of
Jill’s design to Jack’s design.
Part 4: Run the permutation test for the Yankees 1927 data, based on home runs, as opposed to runs.