What effect does increasing the sample size have on the width of a confidence interval? I know that increasing the sample size decreases the width of confidence intervals because it decreases the standard error.  But why?

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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What effect does increasing the sample size have on the width of a confidence interval?

I know that increasing the sample size decreases the width of confidence intervals because it decreases the standard error.  But why?

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