## Math 113: Study Guide Chapters 9-10

1. Know the assumptions / properties of Pearson's Linear Correlation Coefficient.
• What values is it between?
• What does a value of zero mean / not mean?
• What happens if you change the scale of either variable?
• What happens if you switch the variables?
• What type of relationship does it measure?
• What type of distribution does it have?
• How many degrees of freedom does it have?
• What type of distribution do the ordered pairs (x,y) have?
2. Know the assumptions / properties of the contingency tables.
• What is the null hypothesis?
• How are the sample data selected?
• What requirement must be met?
• What type of data is used?
• What type of distribution does it have?
• How many degrees of freedom does it have?
• What type of test is it?
3. Know the assumptions / properties of multinomial experiments.
• What is the null hypothesis?
• What requirement must be met?
• What is the sample data?
• What distribution does it have?
• How many degrees of freedom does it have?
• What type of test is it?
4. Know the guidelines for using the regression equation.
• Know the guidelines for using a regression equation from page 501.
• What is the equation that should be used if there is no significant linear correlation (pg 500)?
5. Know the properties of multiple regression.
• When does the largest value of R-square occur?
• When does the largest value of the adjusted R-square occur?
• How is the Analysis of Variance used to test the regression equation?
• How does correlation between independent variables affect the choice of variables?
• What tools can be used to perform multiple regression.
• What are the degrees of freedom?
6. Contingency Table. Write the null hypotheses. Find one (not all of them) expected frequency. Identify the degrees of freedom. The test statistic and p-value are given, state the decision and conclusion.
7. Know what happens to the test statistic of a contingency table when the data is manipulated. Three parts. Do NOT write "the same" but give a numerical answer. Also give a conclusion based on the test statistic and degrees of freedom (use table A-4 to get critical value).
8. Know what happens to the test statistic of a multinomial experiment when the data is manipulated. Two parts. Do NOT write "the same" but give a numerical answer. Also give a conclusion based on the test statistic and the critical value.
9. Know what happens to the linear correlation coefficient when the data is manipulated. Three parts. Do NOT write "the same" but give a numerical answer. Also give a conclusion based on the test statistic and the sample size (use table A-6 to get critical value).
10. The value of the correlation coefficient, r, and the total variation are given. Find the coefficient of determination, explained variation, and unexplained variation.
11. A statistical test that you have never seen and a p-value are given. Give the conclusion.
12. Linear regression problem. The summary statistics are given to you. Look at a scatter plot and determine whether or not there appears to be any linear correlation. Identify the null hypothesis, the correlation coefficient, critical value (table A-6), decision, conclusion. Tell whether or not the regression equation should be used and estimate dependent variable. Use the appropriate equation to estimate a value of the dependent variable. Find the coefficient of determination.
13. Multiple regression problem. A bivariate correlation table from SPSS is given; rank the variables from most correlated to least correlated to the stated variable. The coefficients table from linear regression in SPSS is given; determine which three variables should be eliminated from the model.
14. Use Statdisk to work a test for independence. Find the degrees of freedom, critical value, test statistic, and p-value. State the decision and conclusion.
15. Use Statdisk to perform linear regression. Write the null and alternative hypotheses. Find the value of the correlation coefficient, critical value, and regression equation from Statdisk. State the conclusion. Identify whether or not the regression equation be used. Find the mean value of the dependent variable. Predict the value of the dependent variable for a specified value of the independent variable.
16. Work a chi-square goodness of fit (multinomial experiment) problem using Statdisk. The observed frequencies are given to you. Look at a histogram and determine if the sample has the claimed shape. Give the degrees of freedom, critical value, test statistic, p-value, decision, and conclusion. Interpret the Kolmogorov Smirnov test and Q-Q Plot to determine if the data are normally distributed.

### Notes

• You will need to use your calculator and Statdisk to complete this test.
• Watch your time, it can easily get away from you if you spend too much time on any one problem. Move quickly, answer the ones you know how to do first. Only the last three problems require Statdisk. Do NOT waste your time on the other problems putting them into Statdisk, enough information is already given to you in the problem to answer the questions.
 # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Total Pts 5 5 5 5 5 8 5 4 5 6 4 10 6 8 9 10 100