#3 (due by 11:59pm CST on Saturday, October 10th) Please study Ch6 to finish this homework assignment. You can find out the answers in textbook practice and weekly materials on BlackBoard. Problem set 1: Use the following to answer questions 1-9 (35 points total): The mean age at marriage for respondents in the 2006 General Social Survey is 23.33, with a standard deviation of 6.13. 1. From Data Set 1, calculate the z-score associated with an observed age at first marriage of 25.50 and provide a substantive interpretation of this quantity (4 pts)? 2. From Data Set 1, calculate the z-score associated with an observed age at first marriage of 18 and provide a substantive interpretation of this quantity (4 pts)? 3. From Data Set 1, assume that the z-score associated with a particular age at first marriage is 0.35. If the proportion of the area between this particular age at first marriage and the mean is 0.14, what proportion of respondents experienced their first marriage earlier than this age (4 pts)? 4. From Data Set 1, calculate the observed age at marriage associated with a z-score of -0.72 (2 pts). 5. From Data Set 1, suppose that a person experienced their first marriage at age 23. If the area beyond the z-score associated with age 23 is 0.24, what proportion of respondents experienced their first marriage before age 23 (2 pts)? 6. From Data Set 1, suppose that a person experienced their first marriage at age 23. If the area beyond the z-score associated with age 23 is 0.24, what proportion of respondents experienced their first marriage after age 23 (4 pts)? 7. From Data Set 1, suppose that the proportion of area between the mean and two z-score of 0.35 is 0.14. Calculate the raw scores associated with these two z-scores. What proportions of respondents were first married between these two ages (10 pts)? 8. From Data Set 1, the z-score associated with the top 5 percent of the distribution is approximately 1.65. What is the observed age at first marriage associated with this zscore (3 pts)? 9. From Data Set 1, for a first age at marriage of 33.44, the proportion of area beyond the zscore associated with this age is 0.05. What is the percentile rank for this score (2 pts)? 1 Problem set 2: use the following table to answer questions 10-14 (25 points total): Respondents in the 2006 General Social Survey were asked about the number of siblings they had. The mean number of siblings was 3.76 with a standard deviation of 3.18. 10. From Data Set 2, calculate the z-score associated with 3 siblings and provide a substantive interpretation of this quantity (5pts)? 11. From Data Set 2, calculate the z-score associated with 1 sibling and provide a substantive interpretation of this quantity (5pts)? 12. From Data Set 2, calculate the z-score associated with 2 siblings and provide a substantive interpretation of this quantity (5pts)? 13. Concerning the data in Data Set 2, the standard normal table reports the following information in the table below. Calculate the proportion of respondents who had more than 2 siblings (5pts). Number of Proportion of Area Between Proportion of Area Beyond Siblings Mean and Z Z 2 .21 .29 3 .09 .41 14. Concerning the data in Data Set 2, the standard normal table reports the following information in the table below. Calculate the proportion of respondents who had between 2 and 3 siblings (5pts). Number of Siblings 2 3 Proportion of Area Between Proportion of Area Beyond Mean and Z Z .21 .29 .09 .41 2 Problem set 3: use the following information to answer questions 15-19 (20 points total): A criminologist developed a test to measure recidivism, where low scores indicated a lower probability of repeating the undesirable behavior. The test is normed so that it has a mean of 140 and a standard deviation of 40. 15. What is the percentile rank of a score of 172 (4 pts)? 16. What is the Z score for a test score of 200 (4 pts)? 17. What percentage of scores falls between 100 and 160 (4 pts)? 18. What proportion of respondents should score above 190 (4 pts)? 19. Suppose an individual is in the 67th percentile in this test, what is his or her corresponding recidivism score (4 pts)? 3 Problem set 4: use the following table to answer questions 20-24 (20 points total): The 2008 GSS provides the following statistics for the average years of education for lower-, working-, middle-, and upper-class respondents and their associated standard deviations . Lower class Working class Middle class Upper class Mean 11.36 12.73 14.40 15.49 Standard Deviation 2.96 2.79 3.04 2.95 N 121 676 636 53 20. Assuming that years of education is normally distributed in the population, what proportion of working-class respondents have 12 to 16 years of education (2 pts)? What proportion of upper-class respondents have 12 to 16 years of education (2 pts)? 21. What is the probability that a working-class respondent, drawn at random from the population, will have more than 16 years of education (2 pts)? What is the equivalend probability for a middle-class respondent drawn at random (2 pts)? 22. What is the probability that a lower- or upper-class respondent will have less than 12 years of education (4 pts)? 23. Find the upper and lower limits, centered on mean that will include 50% of all workingclass respondents (4 pts). 24. If year of education is actually positively skewed in the population, how could that change your other answers (4 pts)? 4