Problem 1: Solution: a) Treatment degree of freedom = 3, therefore there are 4 treatments. Total degree of freedom is 30; therefore there are 30 data samples. The experiment design is shown in the following table: Treatments C (9)
Number Replications Besi
1.6 1.6 (a) Consider the following statistical model: yi = + li + i , i=1,2,6, where yi=the ith observed difference between A and B (A-B) =the intrinsic difference between A and B (A-B) li=learning effect of the ith transcript i=errors with mean 0 When th
Problem 1 (a)(b) Its a paired t-test. According to (3.1), we can get: t = -3.08, p = 0.027 Since t5, 0.05/2 = 2.571 < |t|, we reject the null hypothesis R code: > x1=c(8,14,16,19,18,12) > x2=c(11,16,20,18,20,15) > N=length(x1) > d = x1-x2 > s_d=sd(d) > t=
4.2. A against B plot is synergistic if ME ( B | A+ ) ME ( B | A) > 0. Then,
[ME ( B)] [INT ( A, B)] = ME ( B | A+) + ME ( B | A) ME ( B | A+) ME ( B | A) 2 2 = ME ( B | A+ ) ME ( B | A).
2 2
2
2
Therefore ME ( B | A+) ME ( B | A) > 0 INT ( A, B) < ME ( B
4.18 4.18 B1B2=1234*2345=15. So the interaction 15 is confounded with the block effect The main effect 5 will not be
B1B2 and the ability to estimate 15 is sacrificed. affected.
4.19. (a)
b1 : B1 = 123, B2 = 456, B3 = 167 B1 B2 = 123456, B1 B3 = 2367, B2
Problems and Solutions for Stat/ME 424, Spring 2011 First Midterm Examination (Total : 100 points)
This is a closed book exam, except for 2-3 sides of notes. You are allowed to use calculators. There are four problems in this exam. In order to get full c
Stat/ME 424, Spring 2011 Solutions to Problems for Midterm II (Total : 100 points)
This is a closed-book exam, except for several sides of notes. You are allowed to use calculators.
Problem 1 (20 pts) Consider a two-way layout with the model yi j = + i +