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A **confidence interval for a mean **is a range of values that is likely to contain a population mean with a certain level of confidence.

It is calculated as:

**Confidence Interval = ****x +/- t*(s/âˆšn)**

where:

**x:Â**sample mean**t:Â**t-value that corresponds to the confidence level**s:Â**sample standard deviation**n:Â**sample size

This tutorial explains how to calculate confidence intervals in Google Sheets.

**Confidence Intervals Using the t Distribution**

If weâ€™re working with a small sample (n

For example, suppose we want to calculate a confidence interval for the true population mean height (in inches) of a certain species of plant, using a sample of 15 plants:

First, we can calculate the sample mean, sample standard deviation, and sample size:

Next, we can use the following formulas to calculate the lower and upper bound for the 95% confidence interval:

The 95% confidence interval for the true population mean height is **(13.877, 19.457)**.

**Confidence Intervals Using the Normal Distribution**

If weâ€™re working with larger samples ( nâ‰¥ 30), we can assume that the sampling distribution of the sample mean is normally distributed thanks to the Central Limit Theorem.

This means we can instead use the **NORM.S.INV()** function to calculate the critical value to use for the confidence interval.

The following example shows how to calculate a confidence interval for the true population mean height (in inches) of a certain species of plant, using a sample of 30 plants:

The 95% confidence interval for the true population mean height isÂ **(20.571, 26.429)**.

Note that larger confidence levels lead to wider confidence intervals. For example, hereâ€™s how to calculate a 99% C.I. for the exact same data:

The 99% confidence interval for the true population mean height is **(19.650, 27.350)**.

Notice that this 99% confidence interval is wider than the 95% confidence interval we calculated earlier.

**Related:**Â Confidence Level vs. Confidence Interval: Whatâ€™s the Difference?

**Additional Resources**

The following tutorials explain how to calculate confidence intervals using other statistical software:

How to Calculate Confidence Intervals in Excel

How to Calculate Confidence Intervals in R

How to Calculate Confidence Intervals in Python