The National Assessment of Educational Progress (NAEP) includes a mathematics te
ID: 3181480 • Letter: T
Question
The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth-grade students. Scores on the test range from 0 to 500. Suppose that you give the NAEP test to an SRS of 900 8th-graders from a large population in which the scores have mean = 285 and standard deviation = 125. The mean X will vary if you take repeated samples. Suppose that we took an SRS of 1600 8th-graders and found X = 288.
Compared with an SRS of 900 8th-graders, the margin of error for a 95% confidence interval for is
A: either smaller or larger, but we can't say which.
B: Larger
C: Smaller
Explanation / Answer
As sample size increaes margin of error decreases
Margin of error for SRS of 900
=+-z (sigma/sqrt(n)
=1.96(125/sqrt(900)
=8.16
Margin of error for SRS of 1600
=1.96(125/sqrt(1600)
=6.125
Answer B
Larger for SRS of 900
B: Larger
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