1. Analysis of Two-Way Tables Moore IPS Chapter 9 © 2012 W.H. Freeman and Company

2. A table has 4 rows and 5 columns. The degrees of freedom for a test are a. 10 b. 12 c. 20 9.1-1 9.1 Inference for Two-Way Tables (r - 1)(c - 1) = 3 * 4 = 12

3. In the table below we examine the relationship between final grade and the reported hours per week each student said they studied for the course. The size of this table is: a. 4 x 6 b. 5 x 3 c. 3 x 5 9.1-2 9.1 Inference for Two-Way Tables

4. We are interested in comparing the proportions of males and females who feel earning a large salary is very important to them. I surveyed 200 of each gender and recorded their answers to the question as “yes” or “no.” If I analyze the data with both a z test for two proportions and a test of no association, the P-value for the z test: a. will be less than for the test. b. will be the same as for the test. c. will be more than for the test. 9.1-3 The data can be considered as either two proportions or a 2 by 2 table. The two are equivalent. 9.1 Inference for Two-Way Tables

5. A study to compare two types of infant formula was run at two sites, Atlanta and Denver. Subjects at both sites were classified as dropouts if they left the study before the conclusion, or completers if they finished the study. The following table gives the number of dropouts and completers at each site. A chi-square test was performed and the result was  22 = 5.101 with P-value = 0.024. The correct conclusion is: a. Atlanta had a greater dropout rate. b. Denver had a greater dropout rate. c. any differences can be explained by sampling variability. 9.1-4 9.1 Inference for Two-Way Tables Responder DropoutCompleter Atlanta16134 Denver21379

6. In a clinical trial of Nasonex, 200 randomly selected pediatric patients (ages 3 to 11 years old) were randomly divided into two groups. The patients in Group 1 (experimental group) received 100 mcg of Nasonex, while the patients in Group 2 (control group) received a placebo. Of the 100 patients in the experimental group, 30 reported headaches as a side effect. Of the 100 patients in the control group, 80 reported headaches as a side effect. Which of the following could be used to test the hypothesis Ho: p 1 = p 2 versus Ha: p 1 ≠ p 2 ? a. t 2 = F b. z 2 = F c. χ 2 = F d. t 2 = χ 2 e. z 2 = χ 2 9.1-5 9.1 Inference for Two-Way Tables

7. In the table below we examine the relationship between final grade and the reported hours per week each student said they studied for the course. The expected count of those who studied between 5 and 10 hours per week and earned a B for the course is: a. 4.672 b. 4.266 c. 8.265 9.2-1 9.1 Inference for Two-Way Tables

8. When examining the independence of two-way tables using the chi- square test, the null hypothesis is: a. that the row and column variables are dependent. b. that the row and column variables are independent. c. that the row and column variables are equal. 9.2-2 9.2 Formulas and Models for Two-Way Tables

9. The Ecology department head is examining the course evaluations for four different sections of an introductory course taught by different instructors. He would like to know if the opinions of students are homogeneous with respect to the quality of instruction they received from their respective professors. Below are the results: 9.2-3 (part 1) 9.2 Formulas and Models for Two-Way Tables

10. What is the null hypothesis being tested in this case? a. Opinions of students are homogenous with respect to the quality of teaching they received. b. Opinions of students are independent with respect to the quality of teaching they received. c. Opinions of students are not associated with respect to the quality of teaching they received. 9.2 Formulas and Models for Two-Way Tables 9.2-3 (part 2)

11. The Ecology department head is examining the course evaluations for four different sections of an introductory course taught by different instructors. He would like to know if the opinions of students are homogeneous with respect to the quality of instruction they received from their respective professors. Below are the results: 9.2-4 (part 1) 9.2 Formulas and Models for Two-Way Tables

12. What is the expected count of positive ratings for the instructor from section A01? a. 25.17 b. 35.17 c. 15.17 9.2 Formulas and Models for Two-Way Tables 9.2-4 (part 2)

13. The Ecology department head is examining the course evaluations for four different sections of an introductory course taught by different instructors. He would like to know if the opinions of students are homogeneous with respect to the quality of instruction they received from their respective professors. Below are the results: 9.2-5 (part 1) 9.2 Formulas and Models for Two-Way Tables

14. What is the degree of freedom for the appropriate test statistic for the above problem? a. 6 b. 8 c. 12 9.2 Formulas and Models for Two-Way Tables 9.2-5 (part 2) df = (r-1)(c-1)= 2(3) = 6

15. In the table below we examine the relationship between final grade and the reported hours per week each student said they studied for the course. In a test of no association between these variables, we are really studying a model of: a. independence. b. comparing several populations. c. neither a nor b. 9.2-6 9.2 Formulas and Models for Two-Way Tables

16. The table below is referred to as a a. 3 x 6 table. b. 3 x 5 table. c. 2 x 5 table. d. 5 x 2 table. e. 5 x 3 table. 9.2-7 9.3 Goodness of Fit Gender MaleFemale Like Very Much1614 Like Somewhat1318 Neutral1716 Dislike Somewhat32 Dislike Very Much10 Two-way tables are classified as r x c.

17. A die is tossed 60 times and the number of dots appearing on the top face are recorded in the table below. An investigator wants to know if there is enough evidence to indicate that the die is not fair. What is the most appropriate test? a. Chi-square: Independence test b. Chi-square: Comparing several proportions test c. Chi-square: Goodness of fit test 9.3-1. 9.3 Goodness of Fit Top Face123456 # of occurrences 812139117

18. A die is tossed 60 times and the number of dots appearing on the top face are recorded in the table below. An investigator wants to know if there is enough evidence to indicate that the die is not fair. What is the expected number of 3s if the die is fair? a. 6 b. 7 c.10 d. 11. 9.3 Goodness of Fit Top Face123456 # of occurrences 812139117 9.3-2 1/6 * 60

19. A die is tossed 60 times and the number of dots appearing on the top face are recorded in the table below. An investigator wants to know if there is enough evidence to indicate that the die is not fair. What are the appropriate degrees of freedom for the chi-square test? a. 5 b. 6 c.10 d. 12. 9.3 Goodness of Fit Top Face123456 # of occurrences 812139117 9.3-3

20. A die is tossed 60 times and the number of dots appearing on the top face are recorded in the table below. An investigator wants to know if there is enough evidence to indicate that the die is not fair. The value of the chi-square statistic is 2.8. Is there sufficient evidence to conclude that the die is not fair? Use  = 0.05. a. Yes b. No. 9.3 Goodness of Fit Top Face123456 # of occurrences 812139117 9.3-4

21. A die is tossed 60 times and the number of dots appearing on the top face are recorded in the table below. An investigator wants to know if there is enough evidence to indicate that the die is not fair. Using the output provided, is there sufficient evidence to conclude that the die is not fair? Use  = 0.05. a. Yes b. No. 9.3 Goodness of Fit Top Face123456 # of occurrences 812139117 9.3-4c C

22. It is desired to test whether the number of gamma rays emitted per second by a certain radioactive substance is a Poisson random variable. The following data give the results obtained from 150 one- second intervals. The mean was estimated from the data as 2.8 gamma rays per second. Some expected frequencies are given. # of Ga Rays: 0 1 2 3 4 5 6 7 Obs Count: 10 25 32 37 21 16 7 2 Exp freq: 9.1 25.5 13.1 6.1 2.4 The degrees of freedom for the appropriate test statistic is: a. 4 b. 5 c. 6 d. 7. 9.3 Goodness of Fit 9.3-5 k-1-# of parameters estimated = 7-1-1 = 5