# Confidence Interval Calculator

This **Confidence Interval** calculator helps you construct a predetermined level of confidence based on a sample of data.

## What is Confidence Interval?

A confidence interval is a range of values that is calculated from a sample of data and is used to provide an estimate of a population parameter. The confidence interval is constructed using a predetermined level of confidence, which represents the probability that the confidence interval contains the true population parameter.

The width of the confidence interval depends on the level of confidence and the sample size. In general, a higher level of confidence or a larger sample size will result in a wider confidence interval, while a lower level of confidence or a smaller sample size will result in a narrower confidence interval.

Confidence intervals are commonly used in statistics to provide estimates of population parameters and to compare different groups or samples. They are a useful tool for quantifying the uncertainty associated with estimates and for communicating the results of statistical analyses to others.

## Here is an example of how to calculate a confidence interval:

Suppose you are conducting a study to estimate the average weight of adult men in a certain population. You collect a sample of 100 men and calculate their average weight to be 80 kg. You also calculate the standard deviation of the sample to be 10 kg. (Refer to this calculator to determine standard deviation)

**Sample Mean (x)** = 80

**Sample Size (n)** = 100

**Standard Deviation (s)** = 10

Let’s say you want to construct a 95% confidence interval for the average weight of adult men in the population. To do this, you first need to determine the margin of error for the confidence interval. The margin of error is calculated using the following formula:

`Margin of error = t-value * standard error`

where t-value is a value from a t-distribution table that corresponds to the desired level of confidence and the sample size (n), and standard error is the standard deviation (s) of the sample divided by the square root of the sample size:

`Standard error = s/√n`

In this example, the desired level of confidence is 95% and the sample size is 100, so the t-value would be 1.96. The standard error is 10 kg / 10 = 1 kg. Therefore, the margin of error is 1.96 * 1 kg = 1.96 kg.

Next, you can use the margin of error to calculate the confidence interval. The confidence interval is calculated using the following formula:

`Confidence interval = sample mean ± margin of error`

In this example, the sample mean is 80 kg, and the margin of error is 1.96 kg. Therefore, the 95% confidence interval for the average weight of adult men in the population is 80 kg ± 1.96 kg, or 78.04 kg to 81.96 kg.

This means that you can be 95% confident that the true average weight of adult men in the population is within the range of 78.04 kg to 81.96 kg.