$$\newcommand{\reals}{\mathbb{R}} \newcommand{\expect}{\mathbb{E}} \newcommand{\var}{\mathrm{var}}$$

### General Information

The Final Exam will have exactly 30 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. You are allowed the use your textbook, two pages of notes (one-sheet, two-sided) and a calculator. Notes can be either typewritten or handwritten. Please minimize the noise from turning pages during the test. 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.
• Be able to calculate the degrees of freedom for 2-way tables.
• Understand the distinction.
• Know how independence is related to calculating expected cell values.
• Understand the distinction between significance test and goodness of fit test.

### Chapter 12

• Know the purpose of one-way ANOVA: testing equality of means for block (stratified) designs.
• Know the mechanics of calculating the F-statistic and the degrees of freedom.
• Be able to look up P-values in the F-distribution table.
• Be able to formulate the null and alternative hypothesis for one-way ANOVA.

### 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.

### Emphasis

• 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 sampe pooling?
• Replacement vs. no replacement.
• Binomial distribution vs. normal distribution.