Statistics Investigative Task 3 Life After High School? The Great Recession was a global economic decline beginning in December 2007. Considered the worst global recession since World War II, it included both a mortgage and financial crisis, and was characterized by high levels of household debt, high unemployment, and trade imbalances worldwide. The National Bureau of Economic Research announced that the recession in the United States ended in June 2009, but many people remain concerned that the recession continues to have a lasting effect on the job market and education, specifically on those students graduating high school. A polling agency wants to investigate what this year’s high school seniors are planning to do after they graduate. Question #1: The Bureau of Labor Statistics released a report on April 17th, 2013 that stated 66.2% of those 2012 high school graduates enrolled in college. The pollsters hope to estimate the percentage of this year’s seniors planning to attend college with a margin of error no greater than 3.5%. What size sample would suffice if they want to have 95% confidence in the estimate? The pollsters randomly select 5 towns in Central Massachusetts and then randomly select one high school in each town. The guidance department at each of the chosen schools is instructed to ask 100 randomly selected seniors what their current plans are, and to report the results back to the pollsters. The data collected from the 5 schools are summarized in the table. Question #2: Determine a 95% confidence interval for the percentage of seniors planning to go to college this year. Explain carefully what your interval means. Question #3: A study showed that about 4% of 2006 high school graduates enlisted in the military. Do these data suggest that the percentage who enlist is different this year? Test an appropriate hypothesis and state your conclusion. Question #4: A few of the seniors did not respond to the guidance queries, and others said they were undecided. The pollsters believe some of these people might eventually decide to enlist in the military. Suppose that one-quarter of this group also enlist. Would that cause you to change your conclusion in Question #3? Explain. Question #5: Explain, in context, what a Type I error and a Type II error would be. Plans Count College 290 Employment 112 Military 27 Other (travel, parenting, etc) 51 Undecided/No response 20

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