EXAMPLE 7 NAEP quantitative scores

The National Assessment of Educational Progress (NAEP) includes a mathematics test for high school seniors. Scores on the test range from 0 to 300. Demonstrating the ability to use the Pythagorean theorem to determine the length of a hypotenuse is an example of the skills and knowledge associated with performance at the Basic level. An example of the knowledge and skills associated with the Proficient level is using trigonometric ratios to determine length.

In 2009, 51,000 12th-graders were in the NAEP sample for the mathematics test. The mean mathematics score was and the standard deviation of their scores was s = 34. Assume that these 51,000 students were a random sample from the population of all 12th-graders. On the basis of this sample, what can we say about the mean score μ in the population of all 12th-grade students?

The 95% confidence interval for μ uses the critical value z* = 1.96 from Table 21.1. The interval is

= 153 ± (1.96)(0.151) = 153 ± 0.3

We are 95% confident that the mean score for all 12th-grade students lies between 152.7 and 153.3.