# CONFIDENCE

The CONFIDENCE function is used to calculate the confidence interval for a population mean, based on a sample.

## Syntax

=CONFIDENCE(`alpha`

, `standard_dev`

, `size`

)

`alpha` | The significance level used to calculate the confidence level. It represents the probability of observing a sample mean that is beyond the confidence interval if the population mean is as hypothesized. |

`standard_dev` | The standard deviation of the population. |

`size` | The size of the sample. |

## About CONFIDENCE

In the realm of statistical analysis and inferential reasoning, the CONFIDENCE function in Excel emerges as a pivotal tool for practitioners seeking to ascertain the confidence interval surrounding a population mean. It's especially valuable when working with a limited sample size and endeavoring to draw inferences about the larger population based on the observed data points. The calculated confidence interval serves as a range in which the true population mean is likely to fall within a specified level of confidence, providing essential insights for decision-making and hypothesis testing in various domains, including research, quality assurance, and market analysis.

## Examples

Suppose you have a sample with a standard deviation of 12, and you want to calculate the 95% confidence interval for the population mean based on this sample. The CONFIDENCE formula would be: =CONFIDENCE(0.05, 12, 100)

If the sample standard deviation is 8 and the sample size is 50, and you aim to determine the 90% confidence interval for the population mean, you can use the CONFIDENCE function as follows: =CONFIDENCE(0.1, 8, 50)

## Notes

It's crucial to ensure that the sample used for the calculation is representative of the population being studied. Additionally, the assumptions of the confidence interval calculation, such as the normality of the population distribution and the standard deviation being known, should be considered when interpreting the results.

## Questions

**What is the purpose of calculating the confidence interval with the CONFIDENCE function?**

The CONFIDENCE function aids in determining the range within which the true population mean is likely to lie, based on the observed sample data. It provides a measure of the uncertainty surrounding the estimate and supports informed decision-making.

**How does the significance level (alpha) affect the confidence interval?**

The significance level (alpha) influences the width of the confidence interval. A higher significance level leads to a wider confidence interval, indicating a greater level of confidence but with a broader range of potential population means.

**In what scenarios is the CONFIDENCE function particularly useful?**

The CONFIDENCE function is valuable when working with sample data and desiring to make inferences about the population mean. It's commonly employed in fields such as market research, quality control, and scientific studies to assess the reliability of estimates and draw conclusions about the larger population based on limited sample information.

## Related functions

T.INV.2T

Z.TEST

CONFIDENCE.NORM

CONFIDENCE.T