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Chapter 8: Q. 56 (page 518)

56. The SAT again High school students who take the SAT Math exam a second time generally score higher than on their first try. Past data suggest that the score increase has a standard deviation of about 50 points.
How large a sample of high school students would be needed to estimate the mean change in SAT score to within 2 points with 95% confidence? Show your work.

Short Answer

Expert verified

The mean change in SAT score to within 2points with 95% confidence is n≥2401.

Step by step solution

01

Given information

Past data suggest that the score increase has a standard deviation of about 50 points. To estimate the mean change in SAT score to
within 2 points with 95% confidence.

02

Explanation

Convert the confidence interval 95% into decimal.
95100=0.95
Using table A, calculate the critical value:
zα/2=z(1−0.95)/2=1.96

Note that, Margin of error Eis 2,and, the standard deviation σis 50
Determine the sample size:

localid="1649838874210" E≥zα/2σn

localid="1649838887825" =2≥1.9650n

localid="1649838893763" =2×n≥1.96×50

localid="1649838900904" =n≥49

Remove the square from both sides:
=(n)2≥492
=n≥2401

Hence, the sample size is n≥2401.

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