# Math 113: Study Guide - Chapters 7-8

Questions 1-18 are true-false. You should know the following.

• Properties of the F distribution. Is it symmetric? Does it have negative critical values? What is its mean and standard deviation? What is its relationship to the chi-squared distribution? Does it require degrees of freedom? How do you find a left tail critical value from the table? What do you use the F test for?
• What is the default level of significance?
• What two things are compared in the classical approach to hypothesis testing? What two things are compared in the probability value approach to hypothesis testing?
• What is the relationship between the probability value for a one-tail test and a two-tail test?
• Know that a sample must be from an essentially normal population to use the student's t, chi-squared, and F distributions.
• When does the central limit theorem apply? When can the binomial can be approximated using the normal?
• How can one tell from a histogram whether or not the data is normal? What is the Anderson-Darling test used for? How does one interpret the Anderson-Darling test? What is a probability plot (quantile-quantile plot) used for? How does one interpret the probability plot?
• What is the mean of a chi-squared distribution?

Here is a problem by problem description for the rest of the test.

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, Anderson Darling Test, Probability (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 curve is given. Label the critical region, non-critical region, and critical value(s). Identify the area in the critical and non-critical regions. Write "Reject H0" and "Fail to Reject H0" in the appropriate regions. Identify the distribution and whether it is a left-tail test, right-tail test, or two-tail test.
6. Identify the distribution from the graph. Six parts. Know the binomial, uniform, normal, student's t, chi-square and F distributions.
7. Look at a probability plot (QQ Plot) and determine if the data comes from a the claimed population.
8. 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). Four parts.
9. Given a probability value and level of significance, write the decision. Two parts.
10. An unknown (to you) test is performed and the type of test, critical value, and test statistic are given. Be able to write the decision and conclusion.
11. 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 interpret the results of the Anderson-Darling test for normality.
12. 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)
13. An unknown (to you) hypothesis test is performed and p-value is given. Give the decision and conclusion.
14. A joint frequency table is given to you. Find six probabilities (joint, marginal, conditional, or union) based on the table. Look at the chapter 3-4 test for a review of this. Then 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.
15. 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 is a list of references at the end of the test. This has no bearing on the test, it's just for reference purposes instead of including it with each problem.
• There is a take home exam for this test. It is worth 12 points and is due the day of the in-class exam. The take home test will require Minitab and it would be good practice to do the Minitab part of the classroom activities where it says "you can look it up in the book or use Minitab".

## Corrections to Take Home Exam

• Problem 36 should end with "Find the possible test statistics."
• Problem 39 should read "The test statistic for a two tail hypothesis test is z=-1.873. Find the p-value."

When I originally wrote the test, I had "critical values" instead of "test statistics" and then decided to change it to see if you understood the relationship between the p-value and test statistic as well as the one between significance level and critical value. However, I didn't change the plurality of the word and this is a problem. There can be two critical values. The number of critical values is determined by the type of test: left and right tail tests have one critical value while two tail tests have two critical values. There is only one test statistic however, even for a two tail test. When finding the p-value for a two tail test, you have to pretend that there could have been another test statistic on the other side of the mean and adjust the p-value for the area over there, also, but there is just one test statistic. The problem with 36 is that I didn't tell you whether the test statistic was on the left side or the right side, so you have to figure out what it would be if it was on either side. In problem 39, I gave you the test statistic and it was on the left side. You just have to compensate for the imagined area on the right side.

## Points per problem

 # Pts 1-18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Take Home Total 9 10 3 3 2 7 3 4 8 2 3 4 12 3 10 5 12 100

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Last updated March 29, 2003 9:13 AM