#5 (due by 11:59pm CST on Sunday, March 20th) Please study Ch8 & Ch9 to finish this homework assignment. You can find out the answers in textbook practice and weekly materials on BlackBoard. Also, please familiar with Table 8.1 Confidence Levels and Corresponding Z values (P. 246). Problem set 1: Use the following data to answer questions 1-3 (30 points): Lower class Working class Middle class Upper class Mean 11.61 12.80 14.45 15.45 Standard Deviation 2.67 2.85 3.08 2.98 N 123 697 626 38 The 2010 GSS provides these statistics above for the average years of education for lower-, working-, middle-, and upper-class respondents and their associated standard deviations. 1. Construct the 95% confidence interval for the mean number of years of education for lower-class and middle-class respondents (10 pts)? 2. Construct the 99% confidence interval for the mean number of years of education for lower-class and middle-class respondents (10 pts)? 3. As our confidence in the result increases, how does the size of the confidence interval change? Explain why this is so (10 pts). 1 Problem set 2: use the following information to answer questions 4-8 (25 points total): 4. A sample of 150 U.S. adults is composed of 100 women and 50 men. Estimate the standard error of the proportions for the female population (5 pts)? 5. A sample of 150 U.S. adults is composed of 100 women and 50 men. Estimate the standard error of the proportions for the male population (5 pts)? 6. A sample of 150 U.S. adults is composed of 100 women and 50 men, estimate the confidence interval for the female population with 99% confidence (5 pts)? 7. A sample of 150 U.S. adults is composed of 100 women and 50 men, estimate the confidence interval for the male population with 99% confidence (5 pts)? 8. Provide a substantive interpretation of the following 99 percent confidence interval: (.23, .43) (5 pts). 2 Problem set 3: use the following information to answer questions 9-13 (25 points total): The 2008 General Social Survey contains information on the number of hours worked by a respondent each week. The mean number of hours worked per week is 39.07, with a standard deviation of 12.51. The sample size is 121. 9. Estimate the value of the standard error (5 pts). 10. Calculate a 95 percent confidence interval for these data (5 pts). 11. Provide a one or two sentence interpretation of this result (5 pts). 12. Using this data, provide a hypothetical numerical example which demonstrates that the precision of a confidence interval is in part a function of sample size (for example, increase sample size to 10,000) (5 pts). 13. Using this data, provide a hypothetical numerical example which demonstrates that the precision of a confidence interval is a function of both sample size and the level of confidence (increase to 99%) (5 pts)? 3 Problem set 4: use the following information to answer questions 14-15 (20 points total): Consider the problem facing security personnel at a military facility in the southwest. Their job is to detect infiltrators (spies trying to break in). The facility has an alarm system to assist the security officers. However, sometimes the alarm doesn't work properly, and sometimes the officers don't notice a real alarm. In general, the security personnel must decide between these two alternatives at any given time: H0: Everything is fine; no one is attempting an illegal entry. H1: There are problems; someone is trying to break into the facility. Based on 14. A \"missed alarm\" is a type ____ error, and its probability of occurrence is denoted as ____. Please explain why (10 pts)? 15. A \"false alarm\" is a Type ___ error, and its probability of occurrence is denoted as ____. Please explain why (10 pts)? 4