Question

The SAT is the most widely used test in the undergraduate admissions process. Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800. A researcher from the admissions department at the University of New Hampshire is interested in estimating the mean math SAT scores of the incoming class with 90% confidence. How large a sample should she take to ensure that the margin of error is below 17? (You may find it useful to reference the z table. Round intermediate calculations to at least 4 decimal places and "z" value to 3 decimal places. Round up your final answer to the nearest whole number.)

sample size=?

Answer 1

Maximum = 800

Minimum = 200

Range = maximum - minimum = 800 - 200 = 600

Using Range rule of thumb

Standard deviation = Range / 4 = 600 / 4 = 150

Population standard deviation = = 150

Margin of error = E = 17

Z_/2 = Z_0.05 = 1.645

sample size = n = [Z_/2* / E] ²

n = [1.645 * 150 / 17]²

n = 211

Sample size = n = 211