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Homework answers / question archive / Name: _______________________________ Social Research II Spring 2021 Exam 3 The exam must be completed and submitted on Blackboard by 11:30 a

Name: _______________________________ Social Research II Spring 2021 Exam 3 The exam must be completed and submitted on Blackboard by 11:30 a.m. on Tuesday, May 11. There are two ways to complete and submit the exam: • The preferred way is to fill in the form fields (boxes) on your computer, save, and upload to Blackboard. (Note: Filling form fields is not supported by Blackboard. You must open the document with Adobe Acrobat Reader.) • The alternative way is to print the PDF file, fill-in by hand, scan to a PDF file, and upload to Blackboard. (Note: There are many free scanning apps that you may download to your mobile phone, such as Genius Scan.) Part I. Fill in the blank (50 pts.) 1. Annual income is measured by the number of dollars earned per year. What is the level of measurement? _____________________________________ . 2. In ANOVA, the total sum of squares is composed of the between group sum of squares and the _____________________________________ . 3. In calculating a chi-square statistic, the frequencies we would expect if there were no relationship between the two variables are called the _____________________________________ . 4. Rejecting a null hypothesis when it is actually true is called a : _____________________________________ error. 5. What is the independent variable in the following hypothesis? People with higher levels of education are less racially prejudiced. _____________________________________ . 1 6. A statement predicting the relationship between two variables is called a: _____________________________________ . 7. A _____________________________________ is a range of values defined by the confidence level within which the population parameter is estimated to fall. 8. Social class is measured with the following categories: (1) lower, (2) working, (3) middle, (4) uppermiddle, and (5) upper. What is the level of measurement? _____________________________________ . 9. The _____________________________________ is the name for the level of probability at which the null hypothesis is rejected. 10. The chi-square statistic is based on the difference between observed frequencies and _____________________________________ . 11. What Z score is used in calculating a 99% confidence interval around a mean? _____________________________________ . 12. In ANOVA, the between group sum of squares is the sum of squared deviations between each group mean and the _____________________________________ . 13. In ANOVA, the F statistic is the ratio of the mean square between groups to the _____________________________________ . 14. A _____________________________________ is a sample statistic used to estimate the exact value of a population parameter. 15. The probability associated with the obtained value of a Z statistic is the: _____________________________________ . 16. What is the dependent variable in the following hypothesis? Women have higher life expectancies than do men. _____________________________________ . 2 17. In a bivariate table, the _____________________________________ variable is the column variable. 18. What Z score is used in calculating a 95% confidence interval around a mean? _____________________________________ . 19. In a bivariate table, column percentages should add up to _____________________________________ percent. 20. Failing to reject a null hypothesis when it is actually false is called a : _____________________________________ error. 21. You are testing a hypothesis about the difference between means. One mean is a population parameter and the other mean is a sample statistic for a sub-group within the larger population. The population standard deviation is known. Which test statistic do you calculate to test the hypothesis? _____________________________________ . 22. You hypothesize that people with higher levels of education (measured as: high, medium, and low) are more likely to favor the legalization of marijuana (measured as: for or against). Which test statistic do you calculate to test the hypothesis? _____________________________________ . 23. You are testing a hypothesis about the difference between means. One mean is a population parameter and the other mean is a sample statistic for a sub-group within the larger population. The population standard deviation is unknown. Which test statistic do you calculate to test the hypothesis? _____________________________________ . 24. You hypothesize that the mean annual income level varies across the following three groups: (1) high school graduates, (2) some college, and (3) college graduates. Which test statistic do you calculate to test the hypothesis? _____________________________________ . 25. What is your favorite statistical technique? _____________________________________ . 3 Part II. Calculations (50 pts.) For numbers with three or more numbers to the right of the decimal point, round to the second (hundredths) decimal place. Confidence Intervals Table 1. Descriptive statistics for number of hours worked last week. Number of Hours Worked Last Week N minimum maximum mean standard deviation 890 1 89 40.05 15.00 1. What is the 95% confidence interval for number of hours worked last week? [Show your calculations below. Or show your calculations on a separate paper, scan to a PDF file, and upload to Blackboard.] 2. Provide an interpretation of the 95% CI that you calculated. 4 3. What is the 99% confidence interval for number of hours worked last week? [Show your calculations below. Or show your calculations on a separate paper, scan to a PDF file, and upload to Blackboard.] 4. Provide an interpretation of the 99% CI that you calculated. 5 Z statistic The national mean for SAT scores is 500 with a standard deviation of 100. The principal of MLK High School claims that SAT scores of students at her school are significantly higher than the national mean. The mean SAT scores from a random sample of 70 students at MLK High School is 527. Based on the sample mean can we conclude that the SAT scores at MLK High School are significantly higher than the population mean? (Round numbers to the second (hundredths) decimal place.) 5. State the research hypothesis (one-tailed, directional). 6. State the null hypothesis. 7. Calculate the Z statistic. [Show your calculations below. Or show your calculations on a separate paper, scan, and upload to Blackboard.] 6 8. What is the p value associated with the Z statistic that you calculated? 9. Do you reject or fail to reject the null hypothesis using an alpha level of .05? Why? 10. What do you conclude? 7 Chi-square statistic You are studying the relationship between gender and opinions on capital punishment. You design a survey and collect data from a random sample of 58 individuals. The sample data is distributed as follows in Table 2. Fill in Table 3 and then answers questions 11 to 16. (Round numbers to the second (hundredths) decimal place.) Table 2. Opinion on Capital Punishment by Gender (frequencies). Opinion on Total Capital Male Female Punishment For Capital Punishment 18 9 27 Against Capital Punishment 10 21 31 Total (N) 28 30 = 58 Table 3. Calculating Chi-Square Gender and observed Opinion on frequencies Capital fo Punishment Male / for Male / against Female / for Female / against (fo - fe) 2 2 χ = Σ fe expected frequencies fe fo - fe 8 (fo - fe)2 (fo - fe)2 fe 11. The research hypothesis is: H1 = Men are more likely to favor capital punishment than are women. What is the null hypothesis? 12. What is the obtained chi-square statistic (that you calculate)? 13. What are the degrees of freedom? 14. What is the critical chi-square statistic for an alpha of .01 (one-tailed test)? 15. Do you reject or fail to reject the null hypothesis? Why? 9 16. What do you conclude? ANOVA You are doing research on the effects of family and work on stress among married women. You have divided a group of 18 married women into three groups: (1) those who both work and have children, (2) those who have children but do not work, and (3) those who work but do not have children. You collect data on the level of stress (on a scale of 1 to 20, where 1 = least stress and 20 = most stress) experienced by married women. The data are in Table 4. Fill in tables 5 and 6 and then answer questions 17-22. (Round numbers to the second (hundredths) decimal place.) Table 4. Levels of Stress among Married Women Work & Children Children Only 17 12 18 15 10 12 14 10 12 11 14 13 Work Only 10 12 8 14 15 12 Table 5. Work & Children sum of scores mean sum of squared scores overall mean Children Only Work Only SX1 = SX2 = SX3 = X1 = X2 = X3 = SX12 = SX22 = SX32 = 10 Table 6. ANOVA Table Source of Variation Sum of Squares a) Degrees of Freedom b) Mean Square c) d) e) f) F statistic g) Between Groups Within Groups Total [Show the calculations you used to attain the numbers in cells a to g in Table 6. Or show your calculations on separate paper, scan, and upload to Blackboard.] 11 17. What is the research hypothesis? 12 18. What is the null hypothesis? 19. What is the F statistic that you calculated (obtained F statistic)? 20. What is the critical F statistic for an alpha = .01 ? 21. Do you reject or fail to reject the null hypothesis? Why? 22. What do you conclude? 13

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