Question

Two students are in charge of finding how many​ T-shirts to order for the students that want one. Each student collects sample data. The conclusions are shown. Compare the​ students' conclusions. Whose inference do you agree​ with? Explain. If there are 525 students in the​ school, use the better conclusion to estimate the number of​ T-shirts the school should order.
Student​ 1: Systematic ​sample; StartFraction 30 Over 50 EndFraction
said they would like a​ T-shirt, so order enough for 60​% of the school.
Student​ 2: Simple random ​sample; StartFraction 51 Over 60 EndFraction
said they would like a​ T-shirt, so order enough for 85​% of the school.
Question content area bottom
Part 1
Whose inference do you agree​ with? Explain.
A.
Student 1 because the systematic sample better represents the population of students.
B.
Student 2 because the simple random sample better represents the population of students.
C.
Both Student 1 and Student 2 because both samples represent the population of students.

Answer 1

Answer: B.

Reason: A simple random sample is less likely to be biased and therefore better represents the population than a systematic sample (which can be biased if there is a hidden pattern). Also Student 2’s sample is slightly larger (60 vs. 50), giving more precision.

Estimate: 0.85 × 525 = 446.25, so about 446 students (round up to 447 shirts if you want to be sure there are enough).