Illuminating Statistical Analysis Using Scenarios and Simulations

12Judging Opinion Split Differences

Statistical Scenario—Surveying for Differences

A survey was conducted in the Flowing Wells (FW) community in which 100 random members were asked their opinion of a new state sales tax policy. The same survey was conducted in the Artesian Wells (AW) community asking 100 random members their opinions. Which of the sample proportion differences for the two communities shown in Table 12.1 might reasonably lead you to believe that there is a difference in the overall opinion split between the two community populations? Just use your intuition.

Table 12.1 Various sample proportion differences.

Sample proportion differences between the two communities (FW sample proportion minus AW sample proportion)

0.05 (e.g., 0.55–0.50)

0.10

0.15

0.20

0.25

Null hypothesis:No difference between the FW and the AW communities' population proportions. That is, the difference between the FW and the AW population proportions equals zero.

Rephrasing: How likely is it to get each of the sample proportion differences if in fact the difference between the FW and the AW population proportions equals zero?

The null hypothesis is that there is no difference between the FW and the AW communities' population proportions, so let's look at simulation results that assume this is true. We'll assume that both Flowing Wells and Artesian Wells have an overall community population opinion with 50% (0.50) agree. If we randomly surveyed 100 people in each of the two ...