Discussion : Understanding Polls-Confidence Interval
Many newspapers, when reporting results of political polls, say that "with 95% confidence, the results are in error by no more than +/- 3 percentage points."
The typical sample size is about 1,500. This allowance for error is intended to cover both sampling variability and the effect of small biases.
1. Assume that the poll (sample) indicates that just about 50% of likely voters favor a particular candidate. How large a +/- term is required for a 95% confidence interval for the population proportion?
2. Would the +/- term be much different if 40% of likely voters in the sample favored the candidate?
3. Why is the quoted +/- 0.03 larger than the +/- term you calculated in Question 1?
NOTE for this Discussion:
Discussion Outcome.
Understand and be able to construct confidence intervals for the mean, and its interpretation and uses. Develop critical thinking regarding confidence intervals.
Understanding Polls - Confidence Interval
Many newspapers, when reporting results of political polls, say that "with 95% confidence, the results are in error by no more than +/- 3 percentage points." The typical sample size is about 1,500. This allowance for error is intended to cover both sampling variability and the effect of small biases
Assume that the poll (sample) indicates that just about 50% of likely voters favor a particular candidate. (Wilkinson et al., 1999).
How large a +/- term is required for a 95% confidence interval for the population proportion?
Solution
Using the formulae
Marginal error = +/-0.025
1. Would the +/- term be much different if 40% of likely voters in the sample favored the candidate? If 40% of likely voters in the sample favored the candidate, the marginal error will be: -
From the results arrived at, the term will not be much different if 40% of the voters favor the candidate. At this point, it is interesting to indicate that a candidate's lead is greater than what we would expect from sampling error, or that a race is "a statistical tie (Bevington & Hill, 1969).
2. Why is the quoted +/- 0.03 larger than the +/- term you calculated in Question 1?
quoted +/-0.03 is larger than the calculated +/- term due to rounding off error. The calculated term is 0.025 which can be rounded off to 0.03.
References
WILKINSON, L. AND TASK FORCE ON STATISTICAL INFERENCE, APA BOARD OF SCIENTIFIC AFFAIRS (1999) ‘Statistical Methods in Psychology Journals: Guidelines and Explanations'. American Psychologist, 54, 8, 594-604.
Data Reduction and Error Analysis for the Physical Sciences.' Philip R. Bevington, McGraw Hill (1969).