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Information about Final Exam (now updated for Fall 2012)
Last update: December 9, 2012, 10:11PM.
Review Sessions
I will hold my regular office hours on Monday, December 10.
In addition, I will conduct two review sessions:
Room  Date  Time 
Math East 246  Thursday, December 6  46PM 
Math (Main Bldg) Room 402  Wednesday, December 12  46PM 
Lastminute comments
IMPORTANT: Please select according to section!
General Information
The Final Exam will have
approximately 20 questions. The
amount of calculations neede will be similar to prior tests.
The Final Exam is comprehensive. Thus, all topics covered in the
course may be used as the base for the Final Exam, with some
emphasis on more advanced topics.
Permitted use of books and notes

You are allowed to bring and use your Math 263 textbook.
and 1 standardsize notebook with notes, handwritten or
typed, with any content of your choice.

If you purchased your textbook as an eBook, you are allowed to
use an electronic book reader or laptop solely for the purpose
of perusing the textbook.

You are permitted to use an electronic calculator.
Prohibited uses of technology and other resources

The use of computer to access resources other than
the textbook is prohibited.

Any equipment requiring external power source,
such as personal computers, are prohibited.

For the duration of the test, all electronic devices
must be disconnected from all networks.

Receiving help from others or giving help to others during
the test is a violation of the Code of Academic
Integrity.
Topics covered
All topics covered by Midterms 13 may be on the test.
Please review:
Also, there is an additional practice test.
The solutions WILL NOT BE POSTED.
In addition, the following topics covered after Midterm 3
may be on the test:
Chapter 9

Be able to calculate the \(\chi^2\) statistic for the
goodness of fit test and independence test.

Be able to calculate the degrees of freedom for 2way tables.

Be able to interpret the joint frequency distribution.

Be able to calculate marginal frequency distributions.

Know how to calculate expected cell values from observed cell
values, i.e. know how to use the rule:
\[\r{expected} = \frac{\r{row total} \times \r{column total}}{\r{sample size}}\]

Understand the distinction between significance test and
goodness of fit test.

Be able to use the table of the \(\chi^2\)distribution in the book
to look up the Pvalue, given the value of the \(\chi^2\)statistic,
and to lookup the critical value of the \(\chi^2\)statistic, given
the confidence or significance level.
Chapter 12

Know the purpose of oneway ANOVA: testing equality of means
for block (stratified) designs. Thus, typically we select an
SRS from a population and assign subjects at random to
treatment groups.

Know the mechanics of calculating the Fstatistic and the
degrees of freedom. You are allowed to have copies of the
blank
ANOVA worksheet and the ANOVA
table formula sheet.

Be able to look up Pvalues in the Fdistribution table. Be
familiar with the layout of the table. If you print out the
table, please make sure that even and odd pages are matching
(only left pages have denominator degree of freedom).

Be able to formulate the null and alternative hypothesis for
oneway ANOVA.

There is one useful formula which expresses the Grand Mean
in terms of group means:
\[\bar{x} = \frac{1}{N}\sum_{i=1}^In_i\bar{x}_i\]
This formula is used when the Grand Mean is not given,
but only group means and sample sizes are.

Note that when the design is balanced
i.e. when all groups are of the same size, we have a
a simpler formula:
\[\bar{x}=\frac{1}{I}\sum_{i=1}^I\bar{x}_i\]
i.e. we simply average the group means to obtain the
Grand Mean.
Familiarity with the terms used in ANOVA
You are expected to know the notations for the quantities used in ANOVA,
as exemplified by the practice problems:
 SSG
 Sum of squares between groups.
 SSE
 Sum of squares of error, or sum of squares within groups.
 SST
 Sum of squares total.
 MSG
 Mean sum of squares between groups.
 MSE
 Mean sum of square within groups.
 DFG
 Degrees of freedom between groups.
 DFE
 Degrees of freedom within groups.
 DFT
 Degrees of freedom total.
 \(R^2\)
 Coefficient of determination
 \(I\)
 The number of groups
 \(n_i\)
 The number of elements in the \(i\)th sample, \(i=1,2,\ldots,I\)
Also, you should know the definitions and fundamental relationships
between these quantities.
Overall emphasis on the final exam

You should be fluent in hypothesis testing fundamentals: formulating the null and alternative
hypotheses for different situations, choosing a suitable statistic, look up of Pvalues
in tables.

You should be absolutely clear which technique to choose for a situation presented
to you. For example, be able to distinguish the following terms:
 Should I use zstatistic or tstatistic?
 Should I use onesample or twosample test?
 Does the situation call for the use of proportions vs. sample means?
 Should I find a confidence interval or conduct a parametric test?
 Should I use a \(\chi^2\) test or oneway ANOVA?
 Boxplot vs. bargraph.
 Mean vs. sample mean.
 Variance vs. Sample variance.
 Should I use sample pooling?
 Replacement vs. no replacement.
 Binomial distribution vs. normal distribution.