
## 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:
RoomDateTime
Math East 246 Thursday, December 6 4-6PM
Math (Main Bldg) Room 402 Wednesday, December 12 4-6PM

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 standard-size 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 1-3 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 2-way 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 P-value, 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 one-way 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 F-statistic 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 P-values in the F-distribution 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 one-way 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 P-values 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 z-statistic or t-statistic?
• Should I use one-sample or two-sample 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 one-way 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.