An upper-level sociology class at a large university has 120 students, including

Question

An upper-level sociology class at a large university has 120 students, including 34 seniors, 57 juniors, 22 sophomores, and 7 freshmen. Imagine that you choose one random student from the classroom (perhaps by using a random number table). What is the probability that the student will be a junior? What is the probability that the student will be a freshman? If you are asked to select a proportionate stratified sample of size 30 from the classroom, stratified by class level (senior, junior, etc.), how many students from each group will there be in the sample? If instead you are to select a disproportionate sample of size 20 from the classroom, with equal numbers of students from each class level in the sample, how many freshmen will there be in the sample?

Explanation / Answer

Solution:

a) = 57 / 120 = 0.475

b) = 7/1 20 =0.0583

c) 30/120*{34, 57, 22, 7} = {8.5, 14.25, 5.5, 1.75}
You could choose {seniors, juniors, sophomores, freshmen} = {9, 14, 5, 2} or {8, 14, 6, 2}.

d) 20/4 = 5 from each class. There will be 5 freshmen in the sample.

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