Question

inferring from a ratio
mr. rodriguez asked 60 randomly chosen students from each grade level at willowbrook school about their favorite types of reading materials. of those 60 students, 12 chose science fiction. mr. rodriguez used the data to draw the inference that about 20% of middle school students prefer to read science fiction. if 150 students attend the school, did he make a reasonable inference? explain.

Explanation:

Step1: Calculate sample proportion

$\frac{12}{60} = 0.2 = 20\%$

Step2: Apply proportion to total students

$20\% \times 150 = 0.2 \times 150$

Step3: Verify representativeness

Sample is randomly selected, so it reflects the population.

Answer:

Yes, Mr. Rodriguez made a reasonable inference. 20% of the randomly selected 60 students chose science fiction, and applying this proportion to the 150 total students gives $0.2 \times 150 = 30$ students, which aligns with the inference. The random sample ensures the proportion is likely representative of the whole school population.