Illuminating Statistical Analysis Using Scenarios and Simulations

7Judging Opinion Splits I

Statistical Scenario—Survey I

Say you want to see if members of your community tend to agree or disagree with a new proposed policy. You decide to survey 30 random community members and record whether each one agrees or disagrees with the new policy. In anticipation, you want to determine an interval you can use for a verdict rule.

Where do you draw the two lines such that if your sample proportion is outside the interval you will reject the null hypothesis of an evenly split community? (One line toward the left and another line toward the right.)

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Proportion of agree

We can put what we now know to use for public-opinion surveying. We'll ask people whether they agree or disagree with something. This agree or disagree item is a binomial variable. Our null hypothesis is that the community is evenly split in opinion, that is, 50% agree and 50% disagree overall. We'll gather our evidence by surveying 30 people. To avoid inadvertent bias when gathering sample opinions for our survey, everyone in the community must have an equal chance of being surveyed. Therefore, we'll select 30 people at random, giving us a random sample of 30 opinions. The 30 opinions serve as our evidence.

This surveying situation is analogous to coin flipping. Given our null hypothesis that the community is evenly split (coin is fair), by randomly selecting each person to survey (each flip) we expect a 0.5 ...