EXAMPLE 6.3

Estimating the mean SATM score for seniors in California. Suppose that you want to estimate the mean SATM score for the 485,264 high school seniors in California.² You know better than to trust data from the students who choose to take the SAT. Only about 38% of California students typically take the SAT. These self-selected students are planning to attend college and are not representative of all California seniors. At considerable effort and expense, you give the test to an SRS of 500 California high school seniors. The mean score for your sample is . What can you say about the mean score μ in the population of all 485,264 seniors?