# Exam 3 Study Guide: Chapters 18-25

1. Given a sample size and sample proportion, find the standard error, critical z values, margin of error, and confidence interval for the population proportion.
2. A confidence interval is given. Find the sample proportion and the margin of error. Use the confidence interval to test a claim.
3. 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. Also, identify whether it is a left tail, right tail, or two-tail test. Look at the figures on page 395 for a start, but most of this is in your notes.
4. Know the concept that is fundamental to all hypotheses testing.
5. A sample size and confidence interval for the population mean are given. Find the sample mean and the margin of error. Find the critical t values and the standard error for the mean. Find the sample standard deviation and conduct a hypothesis test based on the confidence interval. Look at your notes from chapter 23.
6. 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.
7. Five statements are given. For each one, decide whether the statement is the null or alternative hypothesis. These are English statements like "The defendant is innocent", not mathematical ones like "12% of adults wet their bed".
8. Five statements are given. For each one, decide whether it represents a type I or type II error.
9. Four p-values and significance levels are given. In each case, decide whether to reject or retain the null hypothesis.
10. Five 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. These are mathematical statements like "the average adult earns \$35,000 a year". They could be about one or two proportions or means. If there are two samples, be sure to define the subscripts or use subscripts that make sense.
11. Five critical value(s) and test statistics are given. For each case, decide whether it is a left tail, right tail, or two tail test and whether to Reject H0 or Retain H0.
12. Three confidence intervals are given along with a null hypothesis. Decide whether the test is left tailed, right tailed, or two tailed and whether you would reject or retain the null hypothesis.
13. 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.
14. 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.
15. Work a hypothesis test. It could be about a single population mean, two independent samples, or a paired sample. For two samples, decide if the samples are independent or dependent. 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. The test statistic, p-value, and sometimes the degrees of freedom from Minitab are given, use them to find the critical value(s), make a decision, and then complete the conclusion.
16. See #15
17. See #15

## Notes

• There are formulas for the mean and standard error for sample proportions and sample means provided on the test. It is up to you to know how and when to use 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 15 16 17 Total 4 3 6 3 5 6 5 5 4 10 10 6 7 7 7 6 6 100