Polls will often present candidates running for election as winning or losing ba
ID: 3299641 • Letter: P
Question
Polls will often present candidates running for election as winning or losing based on the results of recent surveys. When presenting the poll, there is usually information about a “margin of error.” What does that mean?
For example, consider that one survey, conducted by a professional polling organization, shows Candidate Q with 49% with a plus or minus margin of error of 2 percentage points (usually depicted as ±2%). The same survey shows the other candidate, Candidate Z having an estimated 47% of likely voters and the same margin for error (±2%).
However, consider that another survey taken of the same population in the same day by a different professional polling organization has different results. In this survey, Candidate Z has polled at 49% while Candidate Q, has only polled at 46%. This survey has a 3-percentage-point margin of error (±3%).
Consider the assumptions you would have to make to be able to compare the information given in these polls and explain the differences. Then take your best guess as to who may be ahead in the race.
Give an explanation, listing the assumptions you would have to make to be able to use the information given in the polls and draw conclusions about a potential outcome. Finally, based on what you know about confidence intervals, take your best guess about which candidate you believe is really ahead in the race. Justify your rationale and explain clearly how the assumptions you made affect your prediction.
Explanation / Answer
Assumptions that are to be made before drawing any conclusions are as follows:
1. The samples are independent.the two candidates are independent of each other because the samples of respondents for each of the polling survey were selected at random.
2. Independence assumption:the respondents for each polling survey were selected at random, so they are supposed to be independent.
3. Randomization condition: the respondents of each polling survey were independent, and therefore, it is obvious that randomization condition is followed.
4. 10% condition:the numbers of respondents polled by each organization were certainly less than 10% of that population.
5. Success/failure condition: Assume for both polling organizations, the all x1, n1-x1, x2, n2-x2 [x denote number of events and n denote sample size, 1 and 2 denote two candidates] should be 10 or greater.
Assume the intervals were computed at x% confidence level. Thus, according to first polling organization, with x% confidence, candidate Q has voting percentage between 47% and 51%. Similarly, candidate Z has voting percentage between 45% and and 47%.
According to polling organization2, with y% confidence, candidate Q has voting percentage between 43% and 49%. Similarly, with y% confidence, candidate Z has voting percentage between 46% and 52%.
The interval width for candidate Q are 4% and 6% respectively and for candidate Z are 2% and 6% respectively.
Going by the interval width of two candidates, one can notice that for candidate Q, the interval width are mostly consistent for two polling organizations, wheras, there is difference in interval width for two polling organizations for candidate Z. It seems that Q is may ahead in the race. The success/failure assumption presumes that all x1, n1-x1, x2, n2-x2 [x denote number of events and n denote sample size, 1 and 2 denote two candidates] should be 10 or greater. Since, the actual x and n are unknown, so if they are less than 10, then the success/failure condition will be violated, and prediction based on confidence interval will be incorrect.