EXAMPLE 8 Stratifying a sample of students

A large university has 30,000 students, of whom 3000 are graduate students. An SRS of 500 students gives every student the same chance to be in the sample. That chance is

We expect an SRS of 500 to contain only about 50 grad students— because grad students make up 10% of the population, we expect them to make up about 10% of an SRS. A sample of size 50 isn’t large enough to estimate grad student opinion with reasonable accuracy. We might prefer a stratified random sample of 200 grad students and 300 undergraduates.

You know how to select such a stratified sample. Label the graduate students 0001 to 3000 and use Table A to select an SRS of 200. Then label the undergraduates 00001 to 27000 and use Table A a second time to select an SRS of 300 of them. These two SRSs together form the stratified sample.

In the stratified sample, each grad student has chance

to be chosen. Each of the undergraduates has a smaller chance,

Because we have two SRSs, it is easy to estimate opinions in the two groups separately. The quick and approximate method (page 46) tells us that the margin of error for a sample proportion will be about

75

for grad students and about

for undergraduates.