Question

when jeremy surveyed thirty 7th - grade students at the community pool, he found that 2/15 had not read at least one book during july. he knows there are about 200 7th - grade students in his community, so he infers that about 40 of them did not read any books in july. is that a good inference? explain.

Explanation:

Step1: Calculate expected number

Find the expected number of non - reading students in the community using the proportion from the sample. The proportion of non - reading students in the sample is $\frac{2}{15}$, and the total number of 7th - grade students in the community is 200. The expected number $n$ is calculated by $n=\frac{2}{15}\times200=\frac{400}{15}\approx26.67$.

Step2: Compare with inferred number

Jeremy inferred that about 40 students did not read any books. Since the expected number based on the sample proportion is approximately 26.67 and 40 is significantly higher than this value.

Answer:

No, it is not a good inference. The proportion from the sample of 30 students gives an expected number of non - reading students in the community of about 26.67, which is much lower than the 40 students Jeremy inferred.