Question

About $1100$high school teachers attended a weeklong summer institute for teaching AP Statistics classes. After learning of the survey described in Exercise 56, the teachers in the AP Statistics class wondered whether the results of the tattoo survey would be similar for teachers. They designed a survey to find out. The class opted to take a random sample of $100$teachers at the institute. One of the first decisions the class had to make was what kind of sampling method to use.

a. They knew that a simple random sample was the “preferred” method. With $1100$teachers in $40$different sessions, the class decided not to use an SRS. Give at least two reasons why you think they made this decision.

b. The AP Statistics class believed that there might be systematic differences in the proportions of teachers who had tattoos based on the subject areas that they taught. What sampling method would you recommend to account for this possibility? Explain a statistical advantage of this method over an SRS.

Short answer

(a) Teachers are split up into forty distinct sessions, finding each one would take a long time and effort.

If cluster sampling were used with each distinct session as a cluster, all teachers from a handful of these clusters would be included in the sample.

(b) It is advisable to employ stratified random sampling after include teachers from each subject area in the sample.

Step-by-step solution

Part (a) Step 1: Given information

About $1100$high school teachers attended a weeklong summer institute for teaching AP Statistics classes.

The class opted to take a random sample of $100$teachers at the institute.

Explanation

Because the 1100 teachers are split up into forty distinct sessions, finding each one would take a long time and effort.

If cluster sampling were used with each distinct session as a cluster, all teachers from a handful of these clusters would be included in the sample. This method of sampling would be far more convenient than a basic random sample.

Part (b) Step 1: Given information

About $1100$high school teachers attended a weeklong summer institute for teaching AP Statistics classes.

The class opted to take a random sample of $100$teachers at the institute.

Part (b) Step 2: Explanation

It is advisable to employ stratified random sampling after including teachers from each subject area in the sample.

In this situation, stratified random sampling draws a simple random sample from separate subgroups, which would be every topic area.

This allows us to compare the topic area to the number of tattooed teachers.