A researcher wishes to see if there is a difference between the dropout rate of students who attend two-year colleges and the dropout rate of students who attend four-year colleges. The researcher randomly selects 1000 students, ages 20-23, from each type of college and finds that the dropout rate for students who attend two-year colleges is \(51 \%\) and the dropout rate for students who attend four-year colleges is \(47 \%\).* \(^{*}\) Although it looks like there is a difference in the percents, the researcher decides to use confidence intervals to be more certain. The \(95 \%\) confidence interval for the percent of dropouts for the two-year college students is \(47.9 \%-54.1 \%\), and the \(95 \%\) percent confidence interval for the dropouts for four-year colleges is \(43.9 \%-50.1 \%\).

1. What are the point estimates for the dropout rates?

2. What is the margin of error for the dropout rate for the two-year college students?

3. How does the sample size affect the size of the confidence intervals?

4. Comparing the two confidence intervals, can the researcher conclude that there is a difference in the percents of dropouts for the two-year colleges and the four-year colleges?