The SAT is the most widely used test in the undergraduate admissions process. Sc

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 99% confidence. How large a sample should she take to ensure that the margin of error is below 26? Use Table 1. (Round intermediate calculations to 4 decimal places and "z-value" to 3 decimal places. Round up your final answer to the nearest whole number.)

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 99% confidence. How large a sample should she take to ensure that the margin of error is below 26? Use Table 1. (Round intermediate calculations to 4 decimal places and "z-value" to 3 decimal places. Round up your final answer to the nearest whole number.)

Explanation / Answer

Since range of the distribution is 200 to 800 so according to range rule of

thumb the standard deviaiton of the distribution is

sigma=(800-200)/4=150

Compute Sample Size  

n = (Z a/2 * S.D / ME ) ^2

Z/2 at 0.01% LOS is = 2.576 ( From Standard Normal Table )

Standard Deviation ( S.D) = 150

ME =26

n = ( 2.576*150/26) ^2

= (386.4/26 ) ^2

= 220.8653 ~ 221

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