Explain using the concept of a confidence interval (population proportion)?
41. 2004 Presidential Election "The Gallup organization conducted a poll of 2014 likely voters just prior to the 2004 presidential election. The results of the survey indicated that George W. Bush would receive 49% of the popular vote and John Kerry would receive 47% of the popular vote. The margin of error was reported to be 3%. The Gallup organization reported that the race was too close to call. Use the concept of a confidence interval to explain what this means."
41. 2004 Presidential Election "The Gallup organization conducted a poll of 2014 likely voters just prior to the 2004 presidential election. The results of the survey indicated that George W. Bush would receive 49% of the popular vote and John Kerry would receive 47% of the popular vote. The margin of error was reported to be 3%. The Gallup organization reported that the race was too close to call. Use the concept of a confidence interval to explain what this means."
1 Answer
A "Confidence Interval" is a range of values for which we accept a particular probability that they are non-random.
Explanation:
When we say that we are "95% sure of something" we also mean that there is at least a 5% chance that it is not so. A confidence interval gives us a related range and probability from which to make decisions. The statistics do not change, but the individual's acceptance of one risk level over another may be different.
For example, we may have a 98% "confidence" that a particular (large) range of values will occur. But decreasing the range interval decreases the "confidence" even faster. So if we have 98% confidence that a value will fall between 0 and 100, we may only have a 60% confidence that it will fall between 50 and 80.
Related to election polls, this example shows a "calculated" value of 49% vs. 47%, or 2% points difference. With a statistical "margin of error" in the poll results of only 3% (not bad, in general, and based on the sample size) that means the Confidence Level (not stated here, often 95% for polls) generated a range of error of 3%.
That means that a 2% measurement difference would be indistinguishable from the expected normal variation of up to 3% - hence "too close to call".
