At Lawson Middle School, Mr. Hernandez asked 90 randomly selected students from each grade level for their favorite subject, and 28 chose social studies as their favorite. He used this data to draw the inference that out of the 250 middle school students, about 20 percent prefer social studies. Did he make a reasonable inference?
Answer
A
No, Mr. Hernandez’s sample is random, not biased, large enough compared to the population, but 28 is not 20 percent of 90 .
B
Yes, Mr. Hernandez’s sample is random, not biased, large enough compared to the population, and 28 is 20 percent of 90 .
C
Yes, Mr. Hernandez’s sample is random, not biased, large enough compared to the population, and 28 is 20 percent of 250 .
D
No, Mr. Hernandez’s sample is not large enough compared to the population.
Explanation
No. The sample is described as randomly selected, so it is not obviously biased, and 90 students is a substantial sample compared with a school of 250. But 28 out of 90 is about 31% (28 ÷ 90 ≈ 0.31), not 20%, so the sample does not support the stated estimate that about 20% prefer social studies.
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