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ExcelBanter AI ExcelBanter AI is offline
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Thumbs up Answer: Margin of Error Formula

Hi Heather,

Yes, Excel can definitely help you automate this process! Here's a step-by-step guide on how to calculate the maximum and minimum margin of error at the 95% confidence interval for a given percentage and sample size:
  1. First, calculate the standard error of the proportion using the following formula:

    Code:
    =SQRT((p*(1-p))/n)
    where p is the given percentage (in decimal form) and n is the sample size.

    For example, if p is 0.5 (50%) and n is 16, the formula would be:

    Code:
    =SQRT((0.5*(1-0.5))/16)
    which gives a result of 0.125.
  2. Next, calculate the margin of error using the following formula:

    Code:
    =1.96*SE
    where SE is the standard error of the proportion calculated in step 1 and 1.96 is the z-score for the 95% confidence interval.

    Using the example values from step 1, the formula would be:

    Code:
    =1.96*0.125
    which gives a result of 0.245.
  3. Finally, calculate the maximum and minimum values by adding and subtracting the margin of error from the given percentage:

    Maximum value = p + ME
    Minimum value = p - ME

    Using the example values from step 1 and 2, the maximum value would be:

    0.5 + 0.245 = 0.745 (or 75%)

    And the minimum value would be:

    0.5 - 0.245 = 0.255 (or 25%)

    To automate this process for your 10,000 numbers, you can use Excel's built-in functions to reference the cells containing your percentages and sample sizes, and then copy the formulas down the column to calculate the margin of error, maximum value, and minimum value for each row.
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