Consider the following study and decide which of the four possible conclusions stated is the best conclusion.
It's October 2014 and we're interested in what proportion of the voters in our state will vote for the Democratic candidate for Governor next month. A leading polling organization has done a scientifically-designed poll of 1000 registered voters in the state and found that 48.1% of the sample of registered voters in the state favor the Democratic candidate.
Which of the following best describes a reasonable prediction about the outcome of the election next month? (Notice that I am not saying that only one of these is correct. This is a question to think about, not one where I expect you to fully understand all the possible answers.)
We predict that exactly 48.1% of the voters will vote for the Democratic candidate for Governor next month.
We don't have any idea what percent of the voters will vote for the Democratic candidate for Governor next month.
If there aren't any major public relations upheavals in the next month, we believe that the percentage of the voters who vote for the Democratic candidate for Governor next month will be fairly close to 48.1%.
If there aren't any major public relations upheavals in the next month, we have 95% confidence that the percentage of voters who vote for the Democratic candidate for Governor next month will be 48.1% plus or minus 3%.
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We can use data from a not-very-large sample, if it is taken by using a reasonable sampling method, to estimate a characteristic of a large population.
When we use data from a sample to estimate a characteristic of a population, it is possible to give quite strong information about how accurate that estimate is expected to be.