# Exam 4 Study Guide: Chapters 18-22

1. Describe the sampling distribution for a sample proportion. Use the 68-95-99.7 rule to label a normal model. Discuss your assumptions and conditions. Look at problems 18.3-4, 7-10.
2. Work a hypothesis test for a single population proportion. Write the original claim symbolically and decide if it is the null or alternative hypothesis. Write H0 and H1 and identify it as a left tail, right tail, or two tail test. Identify the values of n and x, and then calculate p-hat. The test statistic and p-value from Minitab are given, use it to make a decision and then write the conclusion. Look at problems 20.7-24.
3. Work a hypothesis test for two population proportions. Write the null and alternative hypotheses and identify it as a left tail, right tail, or two tail test. The output from Minitab is given, use it to answer the questions. Determine whether or not the confidence interval contains the claimed difference, give the value of the test statistic and the p-value. Make a decision and then give a conclusion. Look at problems 22.13-20.
4. Work a hypotheses test. Similar to questions 2 and 3.
5. A confidence interval is given. Find the sample proportion and the margin of error. Use the confidence interval to test a claim. If you took good notes, then look in your notes for chapter 19. Otherwise, look at somebody else's notes.
6. A graph of a probability distribution is given along with a critical value and level of significance. Draw and label a vertical line at the critical value, shade and label the critical region, label the non-critical region, label each region with the area in that region, write "Reject H0" and "Retain H0" in the appropriate regions of the graph. Look at the figures on page 395 for a start, but most of this is in your notes.
7. Three pairs of statements are given. For each one, decide which statement is the null hypothesis and which statement is the alternative hypothesis. These are English statements, not mathematical ones.
8. You are given a test statistic and critical value(s). Decide whether it is a left tail, right tail, or two tail test and whether to Reject H0 or Retain H0. Three parts.
9. Know the concept that is fundamental to all hypotheses testing.
10. Three pairs of statements are given. For each pair, decide which is a type I error and which is a type II error.
11. Two claims are given. For each claim, write the null and alternative hypotheses and determine whether it is a left tail, right tail, or two tail test.
12. Definitions. There are 8 definitions given, you need to supply the term that is best defined. There is no word bank, you need to know the terms.
13. A p-value and significance level are given. Decide whether to reject or retain the null hypothesis. Two parts.
14. A claim is made and a statistical test that you've never seen before is performed. Use the p-value from the test to decide whether to reject or retain the null hypothesis. Complete the conclusion.

## Notes

• Some of the early problems on the test are very similar to those from the text. Later problems are designed to see if you understand the process, there aren't really good problems in the text to look at.
• Problems 2-4 are worth 40% of your test, make sure you know how to do them.
• You will definitely want a calculator.
• When probabilities are asked for, they should be given as decimals.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total 6 13 13 14 5 5 6 6 3 6 6 8 4 5 100