EXAMPLE 6.9 Estimating the Mean SATM Score for Seniors in California

Suppose that you want to estimate the mean SATM score for the 486,549 high school seniors in California.⁷ 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 a simple random sample (SRS) of 500 California high school seniors. The mean score for your sample is . What can you say about the mean score in the population of all 486,549 seniors?