At Brighton Middle School, Mr. Yule asked 50 randomly selected students from each grade level about their favorite subject, and 12 chose science. He used this data to draw the inference that about 25% of middle school students will indicate science is their favorite subject. If there are 200 students all together, did he make a reasonable inference?

Question

At Brighton Middle School, Mr. Yule asked 50 randomly selected students from each grade level about their favorite subject, and 12 chose science. He used this data to draw the inference that about 25% of middle school students will indicate science is their favorite subject. If there are 200 students all together, did he make a reasonable inference?
No, Mr. Yule’s sample is biased and too small to be representative of the population.
Yes, Mr. Yule’s sample is small and biased, so it is representative of the population.
No, Mr. Yule’s percentage is too large. He should have used 6%.
Yes, Mr. Yule’s sample is random and representative of the population.

GPT-4o mini · Answer

To assess whether Mr. Yule made a reasonable inference about the favorite subject of middle school students based on his sample, we need to evaluate the sample size, the method of selection, and whether the sample accurately represents the population.

Sample Size: He surveyed 50 students from each grade level. Assuming there are multiple grade levels (for example, 6th, 7th, and 8th grade), this would result in a total sample size of 150 (50 students * 3 grades). A sample size of 150 can provide some insight, but sample size alone does not determine representativeness.
Bias and Representation: The selection of 50 students from each grade could be seen as a systematic approach and may not inherently introduce bias, unless the method by which these students were chosen was flawed (e.g., if only students from certain classes were included). However, if the grades are combined and different factors affect preference (like grade differences impacting subject interest), one could argue the representation might not capture the whole diversity of opinions across all students.
Percentage: Mr. Yule reported that 12 out of 50 students chose science as their favorite subject, which calculates to 24% (not 25%). This percentage is close, but he rounded it to 25%. For a larger population of 200 students, this extrapolation could suggest that about 48 students might prefer science, assuming the sample is representative.

Taking these factors into account, the appropriate choice based on the provided options would be:

No, Mr. Yule’s sample is biased and too small to be representative of the population.

Although the sample was random, the fact that only students from each grade level were selected could lead to disproportionate representation. Additionally, other factors might influence preference for subjects that weren't accounted for in the sampling method.