## Resampling – Two Population Proportions

On day 7 of instruction in my intro statistics course we spent the class working through a project comparing two population proportions using resampling.

Click here to download a pdf copy of the project: Two Proportion Resampling

**Hands-On First**

Mike Sullivan recommends a hands-on simulation before turning to the computers, so I began by using poker chips for this scenario: *A random sample of 15 students at my college had 9 female students in it (60% female), while a random sample of 8 students at a nearby college had 4 female students in it (50% female). Is this evidence that my college has a higher percentage of females?*

I had 13 red poker chips for the 13 females and 10 white poker chips for the 10 males. You could use 13 red playing cards and 10 black playing cards if you prefer. The idea behind resampling is that if the two schools have the same percentage of female students we can randomly assign each of these 15 of these students to my college to determine how often we observe a sample difference of at least 10%. We picked 15 chips from the bag and kept track of how many times the sample contained at least 9 females. (It happened 4 of the 5 times we did it by hand.) Students, based on the one proportion simulations, immediately knew that this was probably not an unusual result if the two population proportions were equal.

**Turn to the Computer**

I then opened up a StatCrunch urn applet to repeat what we had done with the poker chips. I could quickly generate 1000 repetitions of the experiment, and we observed that my college’s sample had at least 9 females approximately half the time.

Students then used StatCrunch’s Resampling Applet for Two Proportions and investigated two cases where the sample percentages remained the same while the sample size increased. We followed up with a two-tail investigation rather than the right-tail approach we took concerning female students.

**Incorporate Student Data**

We finished the project using two data sets that students had gathered earlier in the week. They had sampled 50 students, recorded their gender, and asked two questions:

- Do you plan to vote in the upcoming election?
- A question of the student’s choice that they felt would produce different results for men and women.

Students then compared the proportion of women who answered yes to the proportion of men who did. Very few of the students were able to conclude that the two population proportions were different, and it gave us a great opportunity to discuss the impact of small samples when dealing with qualitative variables.

**Summary**

It took all of the 50 minutes to get through the project. In the future I might cut out one of the two resampling investigations comparing the percentage of females at the two colleges, and perhaps have the students only ask the one question of the 50 students. I could also spin off their second question into a take home project, with them bringing those results back the next day.

I’d love some feedback on this project, or this approach in general. Let me know what you think. This week we will be taking a look at bootstrapping to estimate a population mean or median and using simulation to determine whether a sample drawn from a population produces an unusual mean.