The American College Health Association produced the National College Health Assessment (Andy Gardiner, "Surfacing from Depression," February 6, 2006). The assessment indicates that the percentage of U.S. college students who report having been diagnosed with depression has risen from 2000. The assessment surveyed 47,202 students at 74 campuses. It discovered that 10.3% and 14.9% of students indicated that they had been diagnosed with depression in 2000 and 2004, respectively. Assume that half of the students surveyed were surveyed in 2004.
a. Conduct a hypothesis test to determine if there has been more than a 0.04 increase in the proportion of students who indicated they have been diagnosed with depression. Use a significance level of 0.05 and a p-value approach to this test.
b. Indicate the margin of error for estimating p1 - p2 with p1 - p2.
c. Determine the smallest difference between the two proportions of students who indicated that they had been diagnosed with depression in 2000 and 2004 that the test in part a would be able to detect.