# Exam 3 Study Guide: Chapters 12-17

1. Know the concept that is fundamental to all hypotheses testing.
2. A confidence interval for the population proportion is given. Find the sample proportion and the margin of error.
3. A sample size and number of successes are given. Find the sample proportion, the standard error for the sample proportion, the margin of error, and the confidence interval. This is like homework 15.
4. A sample size and a confidence interval for the population mean are supplied. Find the sample mean, the margin of error, the standard error the means, and the sample standard deviation.
5. Five claims are given. For each claim, write it symbolically and determine whether it is the null or alternative hypothesis. 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.
6. Three p-values and significance levels are given. In each case, decide whether to reject or retain the null hypothesis.
7. Five claims are written symbolically. Determine whether the given statement is the null hypothesis or the alternative hypothesis.
8. 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". Remember that the null hypothesis is the normal or assumed condition.
9. Five statements are given. For each one, decide whether it represents a type I or type II error. For example, "A blood test comes back negative (not infected) when the person really is infected" is a type II error because the normal condition of a person is that they are not infected. Since they actually are infected, the null hypothesis is false and we are retaining a false null hypothesis.
10. 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.
11. A test statistic and the area to the left, right, and twice the smaller area are given. Circle the correct responses so that the conclusion is properly worded. Three parts.
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. 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. Most of this is in your notes and the graphs from the activities.
14. Work a hypothesis test. It could be about one or two proportions or means. 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 key values from the problem. The test statistic, p-value, and/or confidence interval from Minitab are given, use them to make a decision and then write the conclusion. Look at activities 6 and 7,homework 17, homework 18, homework 19, and homework 20. When you need a critical value, there is a portion of the table given.
15. Similar to #14
16. Similar to #14
17. A joint frequency table is given. Use it to answer the probabilities of certain events occurring.
18. Find the probabilities of multiple events happening. Use the multiplication rule.
19. Find the mean and standard deviation of a discrete probability distribution.
20. Find the mean, standard deviation, standard error for a small set of data. Then find the test statistic based on the claim.
21. Find the mean, median, range, standard deviation, and variance for the indicated transformation.

## Notes

• The formulas for the standard errors of the mean and proportion are given on the exam. You will need to know when to use them.
• You will want a calculator for the test although the hardest calculations involve simple arithmetic.
• Where p-values are given, pay attention to whether they are for a one tail test or a two tail test. You may need to adjust the value depending on what type of value you have.
• You will not need the statistical tables. Where you are asked to find critical values or p-values, portions of the table are supplied.
• You may want to review the hypothesis testing assessment.
• Questions 17-21 are mostly similar to questions you've had on previous exams.
• Make sure you understand the conclusions. Almost 20% of your test is based on properly wording them.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Total 2 2 6 6 10 3 5 5 5 10 9 6 6 15 14 13 6 6 4 8 9 150