Mala Mahadevan explains what confidence intervals are:

Suppose I look at a sampling of 100 americans who are asked if they approve of the job the supreme court is doing. Let us say for simplicity’s sake that the only two answers possible are yes or no. Out of 100, say 40% say yes. As an ordinary person, you would think 40% of people just approve. But a deeper answer would be – the true proportion of americans who approve of the job the supreme court is doing is between x% and y%.

How confident I am that it is? About z%. (the common math used is 95%). That is an answer that is more reflective of the uncertainty related to questioning people and taking the answers to be what is truly reflective of an opinion. The x and y values make up what is called a ‘confidence interval’.

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