ANOVA Notes
Math 481
April 27, 2006
Given k normal populations with a common variance 2 , we wish to perform the
following hypothesis test:
H 0 : 1 = 2 = = k
H1 : i = j for at least one i, j,
where i is the mean of the i-th population; 1 i k .
We will con
Linear Approximations
In this section were going to take a look at an application not of
derivatives but of the tangent line to a function. Of course, to
get the tangent line we do need to take derivatives, so in some
way this is an application of derivat
Types of Infinity
Most students have run across infinity at some point in time prior to a calculus class. However,
when they have dealt with it, it was just a symbol used to represent a really, really large positive
or really, really large negative number
Math 481 Review Problems
Be sure to justify your arguments: point out, for example, where you use linearity of E or independence, show clearly why any cancellations occur, etc. 1. Let X1 , . . . Xn be a random sample from an innite population. (a) Derive
Solutions to Math 481 Review Problems
1. (a) We compute
n n
(Xi )2 =
i=1 i=1 n
(Xi X) + (X )
n
2
n
=
i=1
(Xi X)2 +
i=1
2(Xi X)(X ) +
i=1
(X )2 .
Now
n n n
2(Xi X)(X ) = 2(X ) (
i=1 i=1
Xi
i=1
X)
= 2(X ) (nX nX) = 0, and the result follows. (b) We compute
640:48101
REVIEW PROBLEMS: EXAM 2
FALL 2007
In writing up solutions you should justify your conclusions by giving a clear chain of reasoning. 1. Six observations of a normal population of mean and variance 2 yield the values 20, 24, 25, 21, 23, and 25. In
Solution to review problem 5
5) Random samples of size 10 from two independent normal populations, each having variance 5, yield x1 = 4 and x2 = 4.9. (a) Test the null hypothesis 1 2 at the 5% level. (b) If in fact 1 = 2 1, what is the probability of a ty
640:48101
REVIEW PROBLEMS: FINAL EXAM
FALL 2007
Final Exam: The nal exam will be Tuesday, December 18, from 8:00 P.M. to 11:00 P.M., in the usual classroom. It will be cumulative, covering the entire semester. The exam will be open book: you may use the t
Computing Indefinite Integrals
In the previous section we started looking at indefinite integrals
and in that section we concentrated almost exclusively on
notation, concepts and properties of the indefinite integral. In
this section we need to start thin