# Confidence Interval Calculator

Our online Confidence Interval Calculator helps you in calculating the confidence interval or the margin of error by assuming the sample mean. This tool also enables you to find the confidence interval even if you only have raw data.

## How to Use Confidence Interval Calculator?

The confidence interval calculator on DupliChecker is the best option that enables you to find the confidence interval without making any hard efforts. If you are tired of memorizing complex formulas, then this online Confidence Interval Calculator comes to save you. The following easy steps will enable you to find the confidence interval for population mean by following simple steps.

- Get access to our confidence interval calculator by visiting
- Once you land on our page, enter the sample mean, sample size, and standard deviation in the given boxes.
- Select the confidence level.
- Now, click on the “Calculate” button to initiate the process.
- You will get your desired results within a flash of an eye.

## What is the confidence interval?

A confidence interval is a range of values that are being observed after analyzing the data, measured at an anticipated confidence level that may contain the true value of the parameter being studied. The reliability of the estimation process, but not the degree of certainty that the calculated confidence interval contains the values of the parameter analyzed, is crucial in estimating the confidence level. So, in simple words, we can say that the confidence interval is clearly related to the confidence level. The anticipated confidence level is taken before calculating the confidence interval and specifies the ratio of confidence intervals, that when created given the selected confidence level over a countless number of independent trials, will comprise the actual value of the parameter.

## Factors that Affect Confidence Intervals

The following elements can affect the confidence interval completely, and it is essential to know about them if you want to have in-depth knowledge about confidence interval.

### Sample size

The “n” denotes the sample size in the formula of confident intervals. If the sample size decreases, then the width of confidence interval increases, if all the other factors remain constant. The growth in sample size indicates superior inference as it comprises more information.

### Confidence level

The data quality is a crucial element while using an advanced confidence level, as the low quality of data may increase the margin of error. The confidence level will also decrease if the confidence interval level decreases, given that all other constraints remain fixed.

### Standard deviation

The standard deviation is denoted with S in the population formula. If the standard deviation rises, there will be an increment in the width of the confidence interval. Standard deviation is mainly an approximation of how much data fluctuate logically. Moreover, it is a challenging task to guess the population if the standard deviation is more and an extensive amount of data isn’t available. it is difficult to estimate but possible with our population mean calculator every member or population can be sampled.

## How to calculate the confidence interval?

The conventional process of finding a confidence interval is complex and tedious. You may require a calculator, notepad, and, most importantly, good mathematical knowledge to perform this task. We all know that the formula for finding the confidence interval is X ± ZS/(√n), and it is a little tricky to solve the data by using this formula.

**Calculate 95 Confidence Interval Manually**

n = 30

S = 10

X = 130

Z= Confidence interval = 95%

Here, we are having all the required components to find the confidence interval. The confidence interval of 95% will give us a z score of 1.960, as per the table. Now, we will put these values into the formula.

The formula for calculating confidence interval is:

=X ± ZS√n

= 130 ± 1.960 10√30

= 130 ± 3.577

The confidence interval for this example is from 126.3515 to 134.6485.

Confidence Interval | Z |

80% | 1.282 |

85% | 1.440 |

90% | 1.645 |

95% | 1.960 |

99% | 2.576 |

99.5% | 2.807 |

99.9% | 3.291 |

You may have observed that an ample amount of time is required to find a confidence interval. That’s why the best way to overcome this issue is the use of an online probability calculator tool. In the discussed example, you were asked how to calculate Probability with a probability formula, and it ended up taking a huge amount of time and effort. If you use an online confidence level calculator instead of depending on the manual ways, you can get the accurate results within a flash of an eye.

## Single-Sample Confidence Interval Calculator

This simple probability calculator utilizes a t statistic, and the sample means (M) to produce an interval estimate of a population mean (μ).

The formula for estimation is:

μ = M ± t(sM)

In this formula,

M = sample mean

t = t statistic determined by the confidence level

sM = standard error = √(s2/n)

Here, you can see that the manual method of finding a sample confidence interval is also tedious. Therefore, the easy way to avoid this nuisance is the use of an online probability calculator. The online tool will assist you in finding the confidence interval within a blink of an eye.