Chapter 7.2, Problem 53E

SAT Scores. Each year, thousands of high school students bound for college take the Scholastic Assessment Test (SAT). This test measures the verbal and mathematical abilities of prospective college students. Student scores are reported on a scale that ranges from a low of 200 to a high of 800. Summary results for the scores are published by the College Entrance Examination Board in College Bound Seniors. The SAT math scores for one high school graduating class are as provided on the WeissStats site. Use the technology of your choice to solve the following problems.

1. a. Obtain the standard deviation of the variable “SAT math score” for this population of students.
2. b. For simple random samples without replacement of sizes 1–487, construct a table to compare the true values of σ_x—obtained by using Equation (7.1)—with the values of σ_x obtained by using Equation (7.2). Explain why the results found by using Equation (7.2) are sometimes reasonably accurate and sometimes not.