## Math 113: Study Guide - Final Exam

1. Describe the distribution illustrated.
2. Draw and label vertical lines to identify the mean, median, and mode of the distribution. Look at page 65.
3. Find the mean, standard deviation of a binomial experiment with n and p given. Then, find the probability of a certain number of successes (use the Binomial program on the calculator).
4. Find the critical values for the normal and Student's T distributions. Remember that the critical value notation is always for a right tail test.
5. Given a set of data, find the mean, standard deviation, median, range, and then identify the type of sampling used.
6. Given a probability distribution, find the mean, variance, and standard deviation. Use the Pdist program on the calculator.
7. Given a p-value and an original claim, state the conclusion. Fill in the blank.
8. Explain why the deviations from the mean must be squared when finding the variation. Draw a figure to illustrate. This is from the notes on the derivation of variation, variance, and standard deviation.
9. Given a confidence interval, find the sample mean and perform a two-tailed hypothesis test.
10. Find the probability of a randomly selected individual having a given score and the probability of a mean of a sample having a given score.
11. Definitions - matching. Not all definitions are used, but know the definitions of the following: Alternative Hypothesis, Binomial Experiment, Class Mark, Class Boundary, Conclusion, Confidence Interval, Confidence Limit, Correlation Coefficient, Critical Value, Decision, Degrees of Freedom, Hypothesis, Median, Midrange, Null Hypothesis, Parameter, Probability Distribution, Sample Size, Statistic, Test Statistic, Type I Error, Type II Error.
12. Simple probability problem. Items are in a hat / bag and an item is randomly selected. Find some probabilities.
13. Find the expected value of a game. A simple game is described, determine the payoffs and then compute the expected value (recall the expected value is the same as the mean of a probability distribution).
14. Shade the region and find the area under the standard normal curve. Four parts.
15. Write the null and alternative hypotheses for the given claims. Three parts.
16. Correlation and Regression. A scatter plot is given along with the values of n, r, y bar, and the regression equation. Describe the linear correlation (use table A6). Write the regression model (be sure to use the right equation). Estimate y for a given value of x. Two parts.
17. Essay: Explain the concepts of hypothesis testing. Be thorough. Be sure to get the statement about all hypothesis testing. This is similar to the fill in the blank on the last exam.
18. Essay: Answer one of the following:
1. Compare and contrast variation, variance, and standard deviation.
2. Explain the concept of probability value.
3. Explain the Central Limit Theorem.

### Notes:

• The first part of the final exam will be a take home portion consisting of 23 multiple choice and 29 true-false questions. It will be due the day of the regularly scheduled final exam.
• The second part of the exam is open notebook.
• After approximately an hour, you will be allowed to get into groups of up to three people. However, when you get into groups, you must give up the use of your notebooks, so you may not want to get into groups as soon as it is possible for you to do so.
• Since the test is open notebook, I would certainly have this study guide in the front of the notebook complete with any notes that you wish to make (perhaps write out all of the definitions of the terms and stick it in your notebook).
• If your notes are lacking in any of these areas, please supplement prior to the test.
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