set 2: Use the following information to answer questions 6-14 (30 points): The mean age at marriage for respondents in the 2010 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 26.50 and provide a substantive interpretation of this quantity (2 pts)? 26.50-23.33/6.13=0.52 2. From Data Set 1, calculate the z-score associated with an observed age at first marriage of 16 and provide a substantive interpretation of this quantity (2 pts)? 26.50-16/6.13=1.71 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)? 0.0557 = proportion if I translate into percentage (0.0557*100=5.57%) 4. From Data Set 1, calculate the observed age at marriage associated with a z-score of -0.72 (2 pts). (0.2358*100)= 23.58%, or (0.2358*26.50)=625 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)? (0.4052 * 100) = 40.52% 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)? (0.4052 * 100) = 39.48% 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 proportion of respondents were first married between these two ages (6 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 z-score (4 pts)? 9. From Data Set 1, for a first age at marriage of 33.44, the proportion of area beyond the z-score associated with this age is 0.05. What is the percentile rank for this score (4 pts)? Problem set 3: use the following information to answer questions 15-19 (25 pts 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 2 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 4 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 Siblings Proportion of Area Between Mean and Z Proportion of Area Beyond Z 2 .24 .26 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 Proportion of Area Between Mean and Z Proportion of Area Beyond Z 2 .24 .26 3 .09 .41 Problem set 4: use the following table to answer questions 20-22 (25 pts total): This table displays unemployment information for each region in the United States in March 2013. The unemployment numbers listed in the table are thousands. For example, the Midwest was home to 2,525,600 unemployed residents when data were collected. Unemployment (in thousands) in the United States, 2013: Midwest 2,525.6 West 3,004.6 Northeast 2,240.2 South 4,106.9 15. What are the mean and standard deviation unemployment numbers for all regions (15 pts)? You can use this working sheet to help you answer this question. Region Unemployment# Y-mean Square of (Y-mean) midwest 2525.60 northeast 2240.20 west 3004.60 south 4106.90 16. Using information from Q21, how many regions fall more than 1 standard above the mean (5 pts)? 17. How does this number compare with the number expected from the theoretical normal curve distribution (5 pts)