Fewer students can afford to attend college. Some commentators have suggested that a heightened sense of patriotism may increase military enlistments, while others think that the existence of actual hostilities may deter young people from choosing a military path. A polling organization wants to investigate what this year’s high school seniors are planning to do after they graduate.

1) During the ‘90s about 63% of 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 4%. What size sample would suffice if they want to have 90% confidence in the estimate?

The pollsters randomly select 5 cities in Upstate New York and then randomly selected on high school in each city. The guidance office 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 following table.

Plans

Count

College

289

Employment

112

Military

26

Other (travel, parenting, etc.)

51

Undecided / No response

22

2) Determine a 90% confidence interval for the percentage of seniors planning to go to college this year. Explain in context what your interval means. Make sure you include your checks that the conditions for inference have been met.

3) During the 90’s about 4.5% of high school seniors 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. Make sure you state your null and alternative hypothesis, the test statistic, the P-value, your alpha level, and your conclusion.

4) A few of the seniors did not respond to the guidance queries, and others said they were undecided. Some of the people might eventually decide to enlist in the military. Suppose that half of this small group also enlist. Would that cause you to change your conclusion in Question 3? Make sure you perform another hypothesis test and make sure you state your null, alternative hypothesis, the test statistic, the P-value, your alpha level, and your conclusion.