Math 113: Study Guide - Chapters 7 - 8

1. Definitions (matching). Eighteen parts. Answers may be repeated. Some answers are not used. You should know the definitions / descriptions of: Null Hypothesis, Alternative Hypothesis, Hypothesis, Level of Significance, Level of Confidence, Probability Value, Type I Error, Type II Error, Critical Region, Critical Value, Test Statistic, Independent Samples, Dependent Samples, Kolmogorov Smirnov Test, Q-Q Plot.
2. You are given a pair of statements. Decide which is the null hypothesis and which is the alternative hypothesis. Three parts.
3. You are given a pair of errors. Decide which one is the type I error and which one is the type II error. Three parts.
4. Know the assumption fundamental to all hypothesis testing.
5. A normal curve is given with portions shaded. Label the critical region, non-critical region, and critical value(s).
6. Identify the distribution from the graph. Six parts. Know the binomial, uniform, normal, student's t, chi-square and F distributions.
7. A Kolmogorov Smirnov test was performed with SPSS with several different distributions (normal, uniform, poisson, and exponential) and the resulting p-values are shown. Decide if the data appears to have the distribution claimed. Note: the assumption under the Kolmogorov Smirnov test is that the data has the distribution tested.
8. Look at a probability plot (QQ Plot) and determine if the data comes from a the claimed population.
9. Given the critical value(s) and test statistic, identify the test as left, right, or two-tailed and write the decision (Reject the null hypothesis or Fail to reject the null hypothesis). This is very similar to activity 8. Three parts.
10. An unknown (to you) test is performed and a p-value is given. Be able to write the decision and conclusion based on the p-value. Be able to look at a normal probability plot and determine if the data is normally distributed.
11. Given a probability value and level of significance, write the decision. Two parts.
12. T-F: Is the F distribution symmetric?
13. T-F: What is the mean of an F distribution?
14. T-F: Can the F distribution have negative critical values?
15. T-F: What is the relationship between the F distribution and the chi-square distribution.
16. T-F: What is the default level of significance?
17. T-F: What two things are compared in the classical approach to hypothesis testing?
18. T-F: What two things are compared in the probability value approach to hypothesis testing?
19. T-F: What is the relationship between the probability value for a one-tail test and a two-tail test?
20. T-F: Know that a sample must be from an essentially normal distribution to use the student's t, chi-square, and F distributions.
21. T-F: When does the central limit theorem apply?
22. T-F: When can the binomial can be approximated using the normal?
23. T-F: How can one tell from a histogram whether or not the data is normal?
24. T-F: What is the Kolmogorov-Smirnov or Anderson-Darling test used for?
25. T-F: What is a probability plot (quantile-quantile plot) used for?
26. T-F: What is the F-test used for?
27. T-F: What is the mean of a chi-squared distribution?
28. Write the null and alternative hypotheses for the given claim. The claim could be about one or two means, proportions, variances or standard deviations. Also identify whether the test is a left-tailed, right-tailed, or two-tailed test (based on the alternative hypothesis). Six parts. If you have two samples, be sure to define your subscripts or use appropriate letters (ex: M for male, F for Female)
29. An unknown (to you) hypothesis test is performed and the type of test, critical value, and test statistic are given. Give the decision and conclusion.
30. Use Excel to find a critical Z score. The function you need to use is given on the test.
31. Use Excel to find a critical t score. The function you need to use is given on the test.
32. Use Excel to find a critical χ² score. The function you need to use is given on the test.
33. Use Excel to find a critical F score. The function you need to use is given on the test.
34. Use the student's t table to look up a probability-value when the test statistic is known (read section on p-values and the example on page 404). Portions of the t-table are included on the test.
35. Use the student's t table to find the critical value given the sample size, level of significance, and type of test. Portions of the t-table are included on the test.
36. Use Statdisk to perform a hypothesis test. Write the original claim symbolically and identify whether it is the null or alternative hypothesis; write the null and alternative hypotheses; identify as left, right or two-tailed; give the critical value(s), test statistic, and p-value from statdisk; give the decision; give the conclusion.
37. Use Statdisk to perform a hypothesis test. Write the original claim symbolically and identify whether it is the null or alternative hypothesis; write the null and alternative hypotheses; identify as left, right or two-tailed; give the critical value(s), test statistic, and p-value from statdisk; give the decision; give the conclusion.

Notes

• The tables in the book are not needed for this test.
• There are some problems that require you to use Microsoft Excel on this test. Instructions for opening MS Excel are given on the test, but you should make sure your machine has it loaded on it before the day of the exam.
• There is a list of references at the end of test. This has no bearing on the test, it's just for reference purposes instead of including it with each problem.