SOCI 3163 ASSIGNMENT 6

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Dallas County Community College *

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Sociology

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Jan 9, 2024

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SOCI 3163.50 SOCIAL STATISTICS- Fall/2023 Homework Assignment 6 Frankfort-Nachmias, Leon-Guerrero, and Davis: Chapter 7 Due: _Sunday_, 10/22/23 Points Value: 25 Instructions: Download this word document to your computer and save the file as your last name_Assignment6 (example: Pioneer_Assignment6). Type your answer(s) for each of the questions below. Once completed, upload your homework assignment to the Module 6 Assignment folder under Homework Assignments in Canvas. Emailed assignment will not be graded. Name: 25/25 (ALL OF THESE ARE CORRECT GRADED BY PROFESSOR) 1. Though 70% of women with children younger than 18 years participate in the labor force, society still upholds the stay-at-home mother as the traditional model. Some believe that employment distracts mothers from their parenting role, affecting the well-being of children. a. Respondents of a 2016 survey were asked to indicate their level of agreement to the statement, “A working mother hurts children.” Of the 454 male respondents who answered the question, 21% strongly agreed that a working mother does not hurt children. Construct a 90% confidence interval for this statistic. (2 points) Based on the 2016 survey for male respondents, the confidence interval for this interval constructed on a 90% interval is (0.1786,0.2414) b. Of the 589 female respondents who answered the question, 48% strongly agreed that a working mother does not hurt children. Construct a 90% confidence interval for this statistic. (2 points) Based on the 2016 survey for female respondents, the confidence interval for this interval constructed on a 90% interval is (0.4461,0.5139) c. Why do you think there is a difference between men and women on this issue? (2 points) Module 6 Assignment Page 1 of 4

A working mother hurts children as indicated by the survey data, which can be attributed to a variety of factors. Societal and cultural norms that often promote traditional gender roles, where women are expected to be primary caregivers, may lead men to be more likely to believe that working mothers negatively affect children. In contrast, women, who often bear the primary responsibility for child-rearing and have firsthand experience in balancing work and family, may be more open to alternative models. Personal experiences, education, awareness, media influence, and peer circles also play roles in shaping these beliefs. Overall, the divergence in opinions likely stems from a complex interplay of these factors. The data shows the difference between male and female respondents to this matter. 2. You have been doing research for your statistics class on the prevalence of binge drinking among teens. According to the 2013 Monitoring the Future data, the average binge drinking score for a sample of 965 teens is 1.28, with a standard deviation of 0.85. Binge drinking is defined as the number of times the teen drank five or more alcoholic drinks during the past week. a. Construct the 95% confidence interval for the true average severe binge drinking score. (2 points) Based on the 2013 data for teens for the true average severe binge drinking score, the confidence interval for this interval constructed on a 95% interval is (1.2263,1.3337) b. Your roommate is concerned about your confidence interval calculation, arguing that severe binge drinking scores are not normally distributed, which in turn makes the confidence interval calculation meaningless. Assume your roommate is correct about the distribution of severed binge drinking scores. Does that imply that the calculation of a confidence interval is not appropriate? Why or why not? (2 points) The confidence interval calculation is not entirely inappropriate if the normality assumption is violated, especially with a large sample size. However, the confidence interval should be considered an approximation, and alternative methods may be more appropriate if the non- normality of the data is a significant concern. It's essential to be aware of the underlying assumptions and the potential limitations of your analysis. 3. A social service agency plans to conduct a survey to determine the mean income of its clients. The director of the agency prefers that you measure the mean income very accurately, to within + $500. From a sample taken 2 years ago, you estimate that the standard deviation of income for this population is about $5,000. Your job is to figure out the necessary sample size to reduce sampling error to + $500. Module 6 Assignment Page 2 of 4

a. Do you need to have an estimate of the current mean income to answer this question? Why or why not? (2 points) No, we need to find out the estimate of current mean income because it is not given in the sample size.We need to find sample size by using standard deviation and confidence interval. You do not need to have an estimate of the current mean income to determine the necessary sample size. When calculating the required sample size to estimate a population mean with a specified level of precision in this case, within +$500, you primarily need information about the desired level of precision margin of error, the population standard deviation, and the desired level of confidence. The current mean income is not a critical factor in this calculation b. What sample size should be drawn to meet the director’s requirement at the 95% level of confidence? (Hint: use the formula for a confidence interval and solve for N, the sample size.) (2 points) The sample size that should be drawn at the 95% level is 384 c. What sample size should be drawn to meet the director’s requirement at the 99% level of confidence? (2 points) The sample size that should be drawn at the 95% level is 664 4. Throughout the 2016 Presidential election primaries, Millennials (those aged 20 to 36 years) consistently supported Senator Bernie Sanders over Secretary Hillary Clinton. According to the 2016 Gallup poll of 1,754 Millennials, 55% had a favorable opinion of Sanders compared to 38% of Hillary Clinton. Calculate the 99% confidence interval for both reported percentages. (4 points, 2 points for each percentage) Sanders 55% favorable opinion is ( 0.5194, 0.5806) Module 6 Assignment Page 3 of 4

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Clintons 38% favorable opinion is ( 0.3501, 0.4098) 5. According to a report published by the Pew Research Center in 2012, 68% of Millennials (Americans in their teens and 20s) think that their generation has a unique and distinctive identity (N=615). a. Calculate the 95% confidence interval to estimate the percentage of Millennials who believe that their generation has a distinctive identity as compared with the other generations (Generation X, baby boomers, or the Silent Generation). (2 points) (65%, 70%) b. Calculate the 99% confidence interval. (2 points) (I did not know if you wanted this as a percent or decimal so I provided both?) (64%,71%) (0.6431,0.7169) c. Are both these results compatible with the conclusion that the majority of Millennials believe that they have a unique identity that separates them from the previous generations? (1 point) Yes, as both intervals are greater than 50%. These results are compatible with the conclusion that the majority of millennials who believe that they have a unique identity that separates them from previous generations. Module 6 Assignment Page 4 of 4

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