In an election year, we have and will see poll results: Candidate x has a 45% positive rating, Candidate y a 53% positive rating, with 2% undecided. Possible er

Question

In an election year, we have and will see poll results: Candidate x has a 45% positive rating, Candidate y a 53% positive rating, with 2% undecided. Possible error is 5%.




What does the 5% mean in relation to Confidence Level?

(Hint: You might want to use an equation to help explain this.)

Answer 1

Statistics is based on both assumptions and math.

 

First, a "poll" is a sampling of a population.  It is assumed that the sampling (polling) method is "fair" (that is, the probability of selecting a person having any of the three opinions -- favorable to x, favorable to y, and undecided -- is the same as the frequency distribution of the population -- favorable to x, favorable to y, and undecided.

 

Of course, mathematically, the actual sample (not the method) may have a (slightly, we hope) different distribution than the population from which it was taken.  That can be calculated mathematically,  Since probability is defined as (number of successful results)/(number of possible results), we can talk about the probability that the sample does, in fact, agree with the population.

 

From a stat dictionary:  "A confidence level refers to the percentage of all possible samples that can be expected to include the true population parameter."

 

Often, the statistics specify a confidence level (often 95%).  Using the math of probabilities and frequency distribution, we are 95% sure that the true population distribution -- for x, for y, undecided -- is within 5% of the numbers of the sample (45%, 53%, and 2%).  That's because 95% of all possible samples match the population.

 

PLZ don't confuse the 95% confidence level and the 5% margin of error.  The statement could have said, "Possible error is 3%."  Then, we would be 95% confident (which means that 95% of the samples match the population) that the actual values of the population are within 3% of those of the sample.

 

So, "What does the 5% mean in relation to Confidence Level?"  Well, at the specified confidence level (95% or 90% or 97% or ...), (95% or 90% or 97% or ...) of the possible poll (sample) results are within 5% of the values of the actual population.

 

An important note on the problem statement:  This problem presents a population and a sample that has a positive rating for EITHER one or the other candidate (but not both) or is undecided.