AP Statistics



Confidence Interval Formulas:

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Using Standard Deviation of a Sample

Conf Interval-Low Boundary = Mean - (z-value)(Standard Deviation) / (square root of sample size)

Conf Interval-High Boundary = Mean + (z-value)(Standard Deviation) / (square root of sample size)


Using Standard Deviation of the Underlying Population

Conf Interval-Low Boundary = Mean - (z-value)(Standard Deviation)

Conf Interval-High Boundary = Mean + (z-value)(Standard Deviation)


Margin of Error - Population Standard Deviation Known

(z-value)(Standard Deviation)


Margin of Error - Population Standard Deviation Unknown, using the Sample’s Std Dev

(z-value)(Standard Deviation) / (square root of the sample size)

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z-value Critical Values:
    1.65 90% confidence
1.96 95% confidence
2.58 99% confidence
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