## Math 113: Chapters 7-8 Study Guide

1. Describe in every day language what a Type I or Type II error is.
2. Know which distribution should be used to test the equality of two variances.
3. Know which distribution should be used to test a single variance.
4. Know which distribution should be used to test the equality of two means, dependent case.
5. Know which distribution should be used to test two proportions.
6. Know the default level of significance.
7. Know the definition of the level of significance.
8. Know the definition of the critical value.
9. Know the definition of null and alternative hypotheses.
10. Know the definition of the probability-value.
11. Know the definition of the F-variable.
12. Know the relationship between prob-value, test statistic, level of significance, and critical values.
13. Know the difference between the decision and conclusion as to whether the null hypothesis or original claim is used.
14. Know the difference between critical value and test statistic as far as which is looked up and which is calculated.
15. Know the results from the classical approach and how they differ from the results with the prob-value approach.
16. Know properties of the Standard Normal distribution.
17. Know properties of the Student's T distribution
18. Know properties of the Chi-Square distribution.
19. Know properties of the F Distribution
20. Know which distributions are best used with the classical approach and which are best used with the prob-value approach.
21. Know when to reject the null hypothesis using both the classical and prob-value approaches.
22. Look up the critical values for a test about a single population mean.
23. Look up the critical values for a test about a single population mean.
24. Look up the critical values for a test about a single population variance.
25. Look up the critical values for a test about two population variances.
26. Find the prob-value for a test statistic which isn't a value directly in the table. The best that you will be able to do is to say the prob-value is between two probabilities.
27. Look up the critical value in a chi-square table when the degrees of freedom aren't in the table. You should go to the value in the table which is less likely to reject in error.
28. Tell how you can tell whether the test for a single population mean is a left-tail, right-tail, or two-tail test by looking at the critical value(s).
29. Calculate the test statistic used to test the equality of two population variances (F-test).
30. A claim and level of significance are given. You are told the decision and you need to write the conclusion.

### Notes:

• Problems 1 - 6 are short answer.
• Problems 7 - 15 are true false.
• Problems 16 - 21 are multiple choice
• None of the problems are directly from the text (that I know of).
Here are all the answers to the test.