# Exam 3 Study Guide: Chapters 12-17

1. Know the concept that is fundamental to all hypotheses testing.
2. 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.
3. The summary statistics for a sample are given. Find the margin of error, the confidence interval, and then make a conclusion based on the confidence interval. Look at homework 14.
4. Write the claim symbolically. 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.
5. 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.
6. 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.
7. Find the mean, standard deviation, standard error for a small set of data. Then find the test statistic based on the claim.
8. 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.
9. A joint frequency table is given. Use it to answer the probabilities of certain events occurring. Leave your answers in fraction form.
10. 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.
11. 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.
12. Make a tree diagram and a joint probability table. Find some probabilities based on the table.
13. Work a hypothesis test for a single population mean or proportion. Start with the null and alternative hypotheses. Find the test statistic. Give a conclusion. Look at homework 17 and homework 18.
14. Find the probabilities of multiple events happening. Use the multiplication rule. Four parts. This is like the second half of homework 7.
15. Work a hypothesis test for two population means or proportions. Look at homework 19 and homework 20.
16. Work a hypothesis test for a single population mean or proportion. Start with the null and alternative hypotheses. Find the center and spread. Find the test statistic. Give a conclusion. Look at homework 17 and homework 18.
17. Work a hypothesis test for two population means or proportions. Look at homework 19 and homework 20.
18. A confidence interval for the population proportion is given. Find the sample proportion and the margin of error.
19. Find the mean, median, standard deviation, and variance for the indicated transformation. These may be for a single variable or for a combination of variables. Remember that for a combination of variables, mean(x±y) = mean(x) ± mean(y), var(x±y) = var(x) + var(y), and for finding the standard deviation, you first find the variance and then take the square root.

## Notes

• The formulas for the standard errors of the mean and proportion are given on the exam. The formula for the margin of error is given on the exam. The formula for the shortcut to finding the variation is given on the test. SS(x) = ∑x2-(∑x)2/n. You will need to know when to use the formulas, however. You will need to know the formula for the test statistic: TS = (observed-expected)/spread
• 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.

## Points per problem

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