Applications using Sample Proportions Preview CT-STEM

Setting up for 2 samples

We’re lucky that the Evanston Police Department keeps these sorts of records AND makes them available to the public. We don't have to use sampling in order to estimate the proportion of traffic stops that involve black drivers. But this is a lesson about sampling, SO WE'RE GOING TO PRETEND!

Let’s say we didn’t have all the data that we do have, so we HAD to use random sampling in order to investigate. For the remainder of this lesson, we’re going to pretend that we don’t have the full data, and we’re going to generate random samples in order to simulate real-world sampling.

We’re going to have to use sampling to estimate two different proportions:

1. The proportion of all traffic stops that are of black drivers

2. The proportion of Evanston residents who are black

There are a total of 72,836 residents in Evanston and 22,687 traffic stops made.

Questions

Please answer the questions below.

Question 5.1

Using our omnipotence, we believe that the proportion of black drivers stopped in traffic stops is about 30%. What is the largest sample size you could use to estimate the true proportion of black drivers stopped in traffic stops? Show your calculations. What is the smallest sample size you could use? Jot down these numbers as you're going to need it later on!

Question 5.2

Once again, we'll use our omnipotence to guess that the true proportion of black residents in Evanston is about 17%. What is the largest sample you could take from the entire population in Evanston and still meet all of our conditions? What is the smallest sample size you could use? Show calculations. Jot down this number as you're going to need it later on!

Question 5.3

There's something obviously unrealistic in our pretend scenario. In real life we might not have any idea about the true proportions. What do you think you would do in that case? (we'll answer this question in the next chapter!)

Notes

These notes will appear on every page in this lesson so feel free to put anything here you'd like to keep track of.