Illuminating Statistical Analysis Using Scenarios and Simulations

10Judging Opinion Splits II

Rather than checking whether a community as a whole might be evenly split, let's figure out how to use our sample proportion statistic and confidence interval to determine what the actual overall community opinion split might actually be.

Statistical Scenario—Survey II

Pollster #1 randomly surveyed 100 community members about a proposed new local policy and found that 40 of the 100 agreed with the proposed new policy. The 0.40 sample proportion is the evidence.

Given the sample proportion of 0.40, draw two lines to make an interval that you think should very likely contain the true, but unknown, overall community proportion (the proportion you would get if you surveyed absolutely everyone).

0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
Proportion of agree

Also, in the same community using the same survey and sample size, pollster #2 got a sample proportion is 0.35 and pollster #3 got 0.30. What are their interval lines?

Now, let's say that the proportion of agree for the entire community is actually 0.40. Only omniscient beings know this. We'll use the 0.40 community proportion of agree for a survey sampling simulation. The histogram in Figure 10.1 shows what happened when 1000 independent surveyors each surveyed 100 random community members. The histogram shows the distribution of the 1000 sample proportions.

Figure 10.1

Based ...