The CONFIDENCE.NORM function returns the confidence interval for a population mean, using a normal distribution. The confidence interval is a range of values. Your sample mean, x, is at the center of this range and the range is x ± CONFIDENCE.NORM.
The CONFIDENCE.NORM function syntax has the following arguments:
- Alpha Required. The significance level used to compute the confidence level. The confidence level equals 100*(1 – alpha)%, or in other words, an alpha of 0.05 indicates a 95 percent confidence level.
- Standard_dev Required. The population standard deviation for the data range and is assumed to be known.
Size Required. The sample size.
Example: Let’s look at some Excel CONFIDENCE.NORM function examples and explore how to use the CONFIDENCE.NORM function as a worksheet function in Microsoft Excel:
Suppose we are annoyed with the length of major league baseball games so we sample 100 games, and determine the average length is 170 minutes with a population standard deviation of 15, with alpha = 0.05
The corresponding confidence interval is then 170 ± 2.94 = approximately [167.06, 172.94].
- If any argument is nonnumeric, CONFIDENCE.NORM returns the #VALUE! error value.
- If alpha ≤ 0 or alpha ≥ 1, CONFIDENCE.NORM returns the #NUM! error value.
- If standard_dev ≤ 0, CONFIDENCE.NORM returns the #NUM! error value.
- If size is not an integer, it is truncated.
- If size < 1, CONFIDENCE.NORM returns the #NUM! error value.
If we assume alpha equals 0.05, we need to calculate the area under the standard normal curve that equals (1 – alpha), or 95 percent. This value is ± 1.96. The confidence interval is therefore: