How to Apply Confidence Intervals Using a Normal Distribution

Confidence intervals are statistical tools that allow statisticians and other researchers to gain an insight into the reliability of their statistics. In essence, the confidence interval replaces a point-estimate for a population parameter with a range of estimates, telling the researchers where the true parameter is likely to lie. There are a myriad of ways to apply confidence intervals, but one of the most useful ways is to use the normal distribution. The normal distribution allows you to use a z-value that corresponds directly to your chosen size of the confidence interval.

Instructions

    • 1

      Calculate the mean of your sample. Sum the data points together and divide by the number of data points. This value is the mean of your data. Call it "m."

    • 2

      Calculate the standard deviation of the sample. Subtract the mean from each datum individually. This creates a new set of numbers. Square all of these numbers. Sum the resulting squares. Divide this number by the number of data points in your sample. Finally, take the square root of this number to yield the standard deviation. Call this number "s."

    • 3

      Decide on the size of your confidence interval. The most common sizes are 90 percent, 95 percent and 99 percent. These represent the "confidence" that your confidence interval contains the true parameter that you wish to estimate. Confidence intervals with larger sizes (for example, 99 percent) will be longer. Call your chosen size "alpha."

    • 4

      Find the z-score associated with your confidence interval's size. Use a z-table (available in any basic statistics textbook or online) to find the z-score associated with your alpha-value. Call this value "z."

    • 5

      Calculate the half-size of the confidence interval. Use the formula h = z*s/sqrt(n), where "sqrt" represents the square root function and "n" represents the number of data points in your sample.

    • 6

      Calculate the left-hand side of the confidence interval. Subtract h from m. Call this value "l."

    • 7

      Calculate the right-hand side of the confidence interval. Add h to m. Call this value "r."

    • 8

      Write the confidence interval in mathematical notation. Write [l, r]. This is the confidence interval based on the normal distribution.

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