When Jim surveyed 5 sixth-grade students at the community skating rink, he found that only 1 out of the 5 had completed the science project. He knows there are about 160 sixth-grade students in his community, so he infers that around 32 students have finished their science project. Is this a good inference?
Answer
A
No, Jim did not make a good inference because his sample is too small and may be biased because he only asked students that were at the rink.
B
No, Jim did not make a good inference because his sample is too small and 32 is not in the same proportion to the population as 1 to 5.
C
Yes, Jim made a good inference because 32 is the same proportion to the population as 1 to 5.
D
Yes, Jim made a good inference because most students at the rink were sixth graders.
Explanation
Jim’s calculation is consistent with the sample proportion: 1 out of 5 is 20%, and 20% of 160 is 32. However, asking only five students is a very small sample, and students at a skating rink may not represent all sixth graders in the community. So his estimate may be unreliable; the choice identifying both the small, potentially biased sample is correct.
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