Returns a value that you can use to construct a confidence interval for a population mean. 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. For example, if x is the sample mean of delivery times for products ordered through the mail, x ± CONFIDENCE is a range of population means. For any population mean, μ_{0}, in this range, the probability of obtaining a sample mean further from μ_{0} than x is greater than alpha; for any population mean, μ_{0}, not in this range, the probability of obtaining a sample mean further from μ_{0} than x is less than alpha. In other words, assume that we use x, standard_dev, and size to construct a twotailed test at significance level alpha of the hypothesis that the population mean is μ_{0}. Then we will not reject that hypothesis if μ_{0} is in the confidence interval and will reject that hypothesis if μ_{0} is not in the confidence interval. The confidence interval does not allow us to infer that there is probability 1 – alpha that our next package will take a delivery time that is in the confidence interval.
Syntax
CONFIDENCE(alpha,standard_dev,size)
Alpha is 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 is the population standard deviation for the data range and is assumed to be known.
Size is the sample size.
Remarks
 If any argument is nonnumeric, CONFIDENCE returns the #VALUE! error value.
 If alpha ≤ 0 or alpha ≥ 1, CONFIDENCE returns the #NUM! error value.
 If standard_dev ≤ 0, CONFIDENCE returns the #NUM! error value.
 If size is not an integer, it is truncated.
 If size < 1, CONFIDENCE 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:
Example
Suppose we observe that, in our sample of 50 commuters, the average length of travel to work is 30 minutes with a population standard deviation of 2.5. With alpha = .05, CONFIDENCE(.05, 2.5, 50) returns 0.692952. The corresponding confidence interval is then 30 ± 0.692952 = approximately [29.3, 30.7]. For any population mean, μ_{0}, in this interval, the probability of obtaining a sample mean further from μ_{0} than 30 is more than 0.05. Likewise, for any population mean, μ_{0}, outside this interval, the probability of obtaining a sample mean further from μ_{0} than 30 is less than 0.05.
The example may be easier to understand if you copy it to a blank worksheet.
How to copy an example
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Selecting an example from Help
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A 
B 
Data 
Description 
0.05 
Significance level 
2.5 
Standard deviation of the population 
50 
Sample size 
Formula 
Description (Result) 
=CONFIDENCE(A2,A3,A4) 
Confidence interval for a population mean. In other words, the confidence interval for the underlying population mean for travel to work equals 30 ± 0.692952 minutes, or 29.3 to 30.7 minutes. (0.692952) 
