Question

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 the percentage in the sample

The percentage of students who prefer science - fiction in the sample of 60 students is calculated as $\frac{12}{60}\times100\%$.
$\frac{12}{60}\times100\% = 0.2\times100\%=20\%$

Step2: Estimate the number of students who prefer science - fiction in the whole school

If 20% of the students prefer science - fiction, and there are 150 students in the school, then the estimated number of students who prefer science - fiction is $0.2\times150$.
$0.2\times150 = 30$

Step3: Analyze the inference

Mr. Rodriguez made an inference based on a random sample. Since the sample was randomly chosen from each grade - level, and the calculation shows that if the 20% preference rate holds for the whole school, we would expect 30 students out of 150 to prefer science - fiction. So, his inference is reasonable.

Answer:

Yes, he made a reasonable inference. The sample was random, and based on the 20% preference rate in the sample, we would expect 30 out of 150 students in the school to prefer science - fiction.