Math – Applications for Living VII

Our class, Math119 (Math – Applications for Living) is in the middle of our work on statistics.  The last class included finding a margin of error and a confidence interval for a poll … like those pesky political polls we are constantly hearing about. 

So, here is the situation.  This month’s poll showed 63% of respondents supported one candidate, based on results from 384 people; last month, the same poll reported 58% supported that candidate.  The article stated that the candidate is enjoying the increased support … is that a valid conclusion?

As you know, this relates to two issues.  First, the standard error for a proportion like this is found with the statistical formula:  

Tests of significance are then based on z values for a normal distribution; the most common reference is z = 1.96 … creating a margin of error representing a 95% confidence interval.

In our class (Math119), we use a quick rule of thumb to combine these two ideas into one statement which just uses the sample size — and this rule of thumb works pretty good for the types of proportions normally seen in polls (p values between 10% and 90%).  The rule of thumb for the margin of error is just the reciprocal of the square root of the sample size     

For the poll data, the sample sizes are both about 400.  The rule of thumb gives an estimate of 5%, which is very close to the actual value (approximately 4.7%.  In our class, we make a reference to the presence of the more accurate formula, but we use only this rule of thumb.

In this poll example, we create the confidence interval … and conclude that there is no significant difference between the polls.  The confidence intervals overlap; even though the new poll has a larger number, it is not enough of an increase to be significant (with this sample size).

We also have talked about selection bias and other potential problems with polls, and have begun the process of thinking about the impact of sample sizes on things being ‘significant’ (whether they are meaningful or not).

 
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