# How to Calculate Confidence Intervals in Google Sheets

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/√n)

where:

• xsample mean
• t: t-value that corresponds to the confidence level
• s: sample standard deviation
• n: sample size

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

### Confidence Intervals Using the t Distribution

If we’re working with a small sample (n < 30), we can use the t-Distribution to calculate a confidence interval for a population mean.

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 we’re working with larger samples ( n≥ 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 is (20.571, 26.429).

Note that larger confidence levels lead to wider confidence intervals. For example, here’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.