﻿ CONFIDENCE function

# CONFIDENCE 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. 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, μ0, in this range, the probability of obtaining a sample mean further from μ0 than x is greater than alpha; for any population mean, μ0, not in this range, the probability of obtaining a sample mean further from μ0 than x is less than alpha. In other words, assume that we use x, standard_dev, and size to construct a two-tailed test at significance level alpha of the hypothesis that the population mean is μ0. Then we will not reject that hypothesis if μ0 is in the confidence interval and will reject that hypothesis if μ0 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.

Important   This function has been replaced with one or more new functions that may provide improved accuracy and whose names better reflect their usage. This function is still available for compatibility with earlier versions of Excel. However, if backward compatibility is not required, you should consider using the new functions from now on, because they more accurately describe their functionality.

## Syntax

CONFIDENCE(alpha,standard_dev,size)

The CONFIDENCE 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.

## 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, μ0, in this interval, the probability of obtaining a sample mean further from μ0 than 30 is more than 0.05. Likewise, for any population mean, μ0, outside this interval, the probability of obtaining a sample mean further from μ0 than 30 is less than 0.05.

The example may be easier to understand if you copy it to a blank worksheet.

How do I copy an example?

Important   Do not select the row or column headers.

Selecting an example from Help

2. Press CTRL+C.

3. In Excel, create a blank workbook or worksheet.

4. In the worksheet, select cell A1, and press CTRL+V.

Important   For the example to work properly, you must paste it into cell A1 of the worksheet.

5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

After you copy the example to a blank worksheet, you can adapt it to suit your needs.

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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)

Applies To: Excel 2010, Excel Starter, Excel Online, SharePoint Online

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