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About $1100$high school teachers attended a weeklong summer institute for teaching AP classes. After hearing about the survey in Exercise $50$, 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 for a sample size of $100$teachers. One of the questions on the survey was Do you have any tattoos on your body?

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 鈥減referred鈥� method. With 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.

Step by step solution

01

Part (a) Step 1: Given information

The given data is

02

Part (a) Step 2: Explanation

The $1100$professors are split up into $40$distinct sessions, so finding down each and every one of them (in the sample) will take a long time and effort.

It would be easier to employ cluster sampling with each individual session acting as a cluster, as this would include all of the professors from a few of these clusters. This sampling strategy will be significantly more practical than a simple random sample.

03

Part (b) Step 1: Given information

The given data is

04

Part (b) Step 2: Explanation

Stratified random sampling is the ideal choice if we want to include teachers from all subject areas in the sample.

In stratified random sampling, simple random samples are drawn from different subgroups, where the subgroups in this case are each topic area.

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

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