SOC 303 Quantitative Methods for the Social Sciences Fall 2021 - Assignment #4 Due date: 16 December 2021 (Thursday) The General Social Survey, which is carried out in most years, collects interview data from a random sample of adults living in the United States. Table 1 gives the means, standard deviations, and standard errors for the occupational prestige scores of black and white females based on data from the General Social Survey in 1998, 2000, and 2002. Table 1. Mean Occupational Prestige Scores of Black and White Females: 1998-2002 Black Females White Females 1998 L = 41.19 = 44.66 Sy = 13.08 Sy = 13.72 5.e. = .86 5.e. = .40 (N = 229) (N = 1157) 2000 t = 39.96 44.28 Sy = 13.71 Sy = 14.00 s.e. = .87 s.e. = .41 (N = 247) (N=1139) 2002 4 =41.40 44.79 Sy=13.72 Sy = 13.55 s.e. = .89 5.e. = .41 (N = 236) (N = 1119) Source: General Social Survey 1998, 2000, 2002. 1. Construct 95 percent confidence intervals for the mean occupational scores of a) black females and b) white females in 2000, and explain what each result means. 2. Will a 99 percent confidence interval give a more precise estimate of the mean occupational prestige score of each group? Construct 99 percent confidence intervals for a) black females and b) white females for the same year. 3. Using confidence intervals, evaluate whether the difference in mean occupational prestige scores of black females in 1998, 2000, and 2002 can plausibly be due to sampling error. Explain how you reached your answer. In the second International Assessment of Educational Progress (IAEP) in 1991, 14 countries assessed the mathematics and science achievement of 9-year-olds and 13-year-olds. The samples of 9- and 13-year-olds were merged, and an overall mean and overall standard deviation were calculated. The scale for each test was standardized so that each test had a normal distribution with a range of scores from 0 to 1,000, a mean of 500, and a standard deviation of 100. This method of proficiency scaling means that 9-year-olds and 13-year- olds are evaluated on a single scale. Table 2 shows the mean mathematics and science proficiency scores for students in several of these countries. Table 2. Mean Mathematics and Science Proficiency Scores of 9- and 13-Year-Olds in Six Countries: 1991 Science Proficiency Country Age 9 Age 13 South Korea 460 571 Taiwan 456 563 United States 446 521 Canada 437 533 Soviet Union 434 541 Spain 430 525 Math Proficiency Country Age 9 Age 13 South Korea 473 542 Taiwan 454 545 Soviet Union 447 533 Spain 432 495 Canada 430 513 United States 420 494 Source: U.S. Department of Education, National Center for Education Statistics, The Condition of Education 1996, NCES 96-304, by Thomas M. Smith, Washington, DC, 1996, pp. 88-91. 4. Among 9-year-olds, the average student from which country reached the highest percentile on math proficiency? the lowest percentile? What was the percentile rank of each student? Show calculations. 5. How does the percentile rank of the average American 13-year-old compare to the percentile rank of the average American 9-year-old on math proficiency? Show how arrived at your answer. you 6. If a goal is set to have the average American 13-year-old reach the 60th percentile on math proficiency, by how much will the average math proficiency score have to be raised? Show work. 7. For the average American 13-year-old to catch up to the percentile rank of the average South Korean 13-year-old on science proficiency, what score would be needed? (Hint: This is an easy brainteaser.) SOC 303 Quantitative Methods for the Social Sciences Fall 2021 - Assignment #4 Due date: 16 December 2021 (Thursday) The General Social Survey, which is carried out in most years, collects interview data from a random sample of adults living in the United States. Table 1 gives the means, standard deviations, and standard errors for the occupational prestige scores of black and white females based on data from the General Social Survey in 1998, 2000, and 2002. Table 1. Mean Occupational Prestige Scores of Black and White Females: 1998-2002 Black Females White Females 1998 L = 41.19 = 44.66 Sy = 13.08 Sy = 13.72 5.e. = .86 5.e. = .40 (N = 229) (N = 1157) 2000 t = 39.96 44.28 Sy = 13.71 Sy = 14.00 s.e. = .87 s.e. = .41 (N = 247) (N=1139) 2002 4 =41.40 44.79 Sy=13.72 Sy = 13.55 s.e. = .89 5.e. = .41 (N = 236) (N = 1119) Source: General Social Survey 1998, 2000, 2002. 1. Construct 95 percent confidence intervals for the mean occupational scores of a) black females and b) white females in 2000, and explain what each result means. 2. Will a 99 percent confidence interval give a more precise estimate of the mean occupational prestige score of each group? Construct 99 percent confidence intervals for a) black females and b) white females for the same year. 3. Using confidence intervals, evaluate whether the difference in mean occupational prestige scores of black females in 1998, 2000, and 2002 can plausibly be due to sampling error. Explain how you reached your answer. In the second International Assessment of Educational Progress (IAEP) in 1991, 14 countries assessed the mathematics and science achievement of 9-year-olds and 13-year-olds. The samples of 9- and 13-year-olds were merged, and an overall mean and overall standard deviation were calculated. The scale for each test was standardized so that each test had a normal distribution with a range of scores from 0 to 1,000, a mean of 500, and a standard deviation of 100. This method of proficiency scaling means that 9-year-olds and 13-year- olds are evaluated on a single scale. Table 2 shows the mean mathematics and science proficiency scores for students in several of these countries. Table 2. Mean Mathematics and Science Proficiency Scores of 9- and 13-Year-Olds in Six Countries: 1991 Science Proficiency Country Age 9 Age 13 South Korea 460 571 Taiwan 456 563 United States 446 521 Canada 437 533 Soviet Union 434 541 Spain 430 525 Math Proficiency Country Age 9 Age 13 South Korea 473 542 Taiwan 454 545 Soviet Union 447 533 Spain 432 495 Canada 430 513 United States 420 494 Source: U.S. Department of Education, National Center for Education Statistics, The Condition of Education 1996, NCES 96-304, by Thomas M. Smith, Washington, DC, 1996, pp. 88-91. 4. Among 9-year-olds, the average student from which country reached the highest percentile on math proficiency? the lowest percentile? What was the percentile rank of each student? Show calculations. 5. How does the percentile rank of the average American 13-year-old compare to the percentile rank of the average American 9-year-old on math proficiency? Show how arrived at your answer. you 6. If a goal is set to have the average American 13-year-old reach the 60th percentile on math proficiency, by how much will the average math proficiency score have to be raised? Show work. 7. For the average American 13-year-old to catch up to the percentile rank of the average South Korean 13-year-old on science proficiency, what score would be needed? (Hint: This is an easy brainteaser.)