Before Election Day, a political poll is conducted using randomly selected registered voters from a statewide list of registered voters. Voters selected at random will be asked who they plan to vote for in the gubernatorial election. There will be a margin of error associated with the proportion of voters who prefer the incumbent candidate. For instance, if 39% of voters in the poll say prefer the current governor, we would hope that a similar percentage of all statewide voters on Election Day would indeed vote for the current governor, but the actual proportion of votes on Election Day for this candidate could be higher or lower than 39%.

A margin of error of 3% at the 95% confidence level means that if the current governor is favored by the 39% of the voters in the poll, then the actual results on Election Day are likely to show between 36% and 42% of all voters voting for the current governor. The 95% confidence level means that 95 out of 100 similar polls would contain equal accuracy in predicting an interval in which the actual Election Day results will occur.

The margin of error is directly proportional to the critical z-score, a value which changes when the confidence level is changed. The critical z-score values are given in the table below, which shows, for example, that when a confidence level of 95% is used, the critical z-score value used to calculate the margin of error is 1.960.

.674 | .841 | 1.036 | 1.282 | 1.645 | 1.960 | 2.054 | 2.326 | 2.576 | 2.807 | 3.091 | 3.291 |
---|---|---|---|---|---|---|---|---|---|---|---|

50% | 60% | 70% | 80% | 90% | 95% | 96% | 98% | 99% | 99.5% | 99.8% | 99.9% |

__Confidence Level C__

The margin of error is also inversely proportional to the square root of the number of people who respond to the poll.

If a confidence level of 99% instead of 95% was desired to have a poll that would correctly predict the Election Day outcome in 99 out of 100 cases, by what factor would the margin of error increase?

Keeping a confidence level of 95%, by what factor would the margin of error be reduced if the number of people participating in the poll was increased by a factor of 3?

Factor of increase

Factor of decrease

Factor of increase

Factor of decrease

0.62

Factor of increase

Factor of decrease

1.04

Factor of increase

Factor of decrease

1.31

Factor of increase

Factor of decrease

1.73

Factor of increase

Factor of decrease

2.576

Factor of increase

Factor of decrease

3.00

Factor of increase

Factor of decrease

9.00

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