Preview - Sampling Distributions 2021

Formulas and Calculations

Here are the formulas for the standard deviation and the mean of a difference between two proportions. Use the model, the known population proportions, and the sampling sizes you calculated before to carry out sampling for both proportions. Scroll down for detailed instructions.

Questions

Please answer the questions below.

Calculate the mean (\(\mu_{\hat {p_1} - \hat {p_2}}\)) and standard deviation (\(\sigma_{\hat {p_1} - \hat {p_2}}\)). This is the center and spread of our sampling distribution for the difference in proportions. 

Set the population proportion to our actual value for proportion of traffic stops of black drivers (0.30). Set the sample size slider to the number you calculated on page 7 for the smallest allowable sample size. Collect a sample, and record your sample proportion (\(\hat p_1\)) here.

Set the population proportion to our actual value for proportion of black resisdents in Evanston (0.17). Set the sample size slider to the number you calculated on page 7 for the smallest allowable sample size. Collect a sample, and record your sample proportion (\(\hat p_2\)) here.

What conclusion(s) would you draw BASED ON YOUR DATA? (We would like you to draw a conclusion about the population from your sample results, using the Normal distribution)

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.