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You can use the CONFIDENCE.NORM function in Excel to calculate the half-width of a confidence interval for a population mean.
This function uses the following syntax:
CONFIDENCE.NORM(alpha, standard_dev, size)
where:
- alpha: The significance level to use (e.g. for a 95% confidence interval you would use .05)
- standard_dev: The population standard deviation, assumed to be known
- size: The sample size
The following example shows how to use this function in practice.
Example: How to Use CONFIDENCE.NORM Function in Excel
Suppose we would like to calculate a 95% confidence interval for the mean height of a particular species of plant.
Suppose we collect a simple random sample of 50 individual plants and find that the sample mean height is 14.5 inches.
Suppose it is also known that the population standard deviation (σ) of height among this species of plant is 3.1 inches.
We can type the following formula into a cell in Excel to calculate the half-width of this 95% confidence interval:
=CONFIDENCE.NORM(0.05, 3.1, 50)
The following screenshot shows how to use this formula in practice:
The half-width for this 95% confidence interval is 0.85926.
To actually construct the confidence interval, we must add and subtract this value to the sample mean.
Thus, the 95% confidence interval for the mean height of this particular species of plant is:
- 95% Confidence Interval: 14.5 ± 0.85926
- 95% Confidence Interval: (13.64074, 15.35926)
The 95% confidence interval for the mean height is between 13.64074 inches and 15.35926 inches.
One interesting thing to note is that the higher the confidence level, the wider the confidence interval will be.
For example, if we wanted to calculate a 99% confidence interval then we would use alpha = 0.01 for the first argument in the CONFIDENCE.NORM function:
=CONFIDENCE.NORM(0.01, 3.1, 50)
The following screenshot shows how to use this formula in practice:
The half-width for this 99% confidence interval is 1.12926.
Thus, the 99% confidence interval for the mean height of this particular species of plant is:
- 99% Confidence Interval: 14.5 ± 1.12926
- 99% Confidence Interval: (13.37074, 15.62926)
Notice that this confidence interval is wider than the 95% confidence interval.