# National Assessment of Educational Progress

1. Estimation of Proportions
2. Education

To track changes over time in the quality of education offered by primary and secondary schools in the U.S., an outfit called the National Assessment of Educational Progress (NAEP) administers tests each year in a variety of subjects to nationwide random samples of students. They actually use cluster sampling rather than simple random sampling, but their method is roughly equivalent to taking an SRS of about 950 students from the population of all U.S. students in a given grade in any given year.

In 1975 the NAEP gave a math test to 17-year-olds. One of the items on the test was as follows:

Do the following addition: 1/2 + 1/3 = ...

617 of the 950 students knew the right answer, 5/6 (the other popular response was 2/5).

Estimate p, the percentage of all 17-year-old students in the U.S. who knew the right answer, attach a give-or-take to your estimate, and construct a 95% confidence interval for p.
If they wanted to be 95% sure of getting the national percentage p right to within 2 percentage points, how many students should they have sampled?

George Michailides
gmichail@stat.ucla.edu