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)