## What is a Confidence Interval?

A confidence interval is an interval that statistician hopes will contain the true parameter value. A confidence interval contains a certain set of possible values of the parameter. A probability that a parameter will between a set of values.

**Key Terms**:

**Probability**: The chance that a particular event will occur.

**Parameter**: A parameter is used to describe the entire population being studied.

In order to understand confidence interval, we need to understand **Sampling** and **Sampling error. A **sample is a collection of objects or observations taken from **Population** of interest. For-example, a population might be all mangoes in garden at a given time. We wish to collect large mangoes and measure them, we cannot measure all so we take sample some of them and measure.

Difference samples of the same population gave different results, this is called sampling error. There will always be sampling error.

we wish to find out how big the mangoes are in garden, We put this as an investigative question:

What is the main weight of all the mangoes in the garden?

We take a sample and calculate the sample mean, i.e., sample mean = 150g. We use a confidence interval to express the range in which we are pretty sure. It is reasonable to say that the mean weight of the mangoes in the garden lies between 148 and 152g.

**What effects the width of Confidence Interval?**

The width of confidence interval depends on two things: Variation within the population of interest and the size of the sample.

If all the values in the population were almost the same, then our sample also have little variation and sample is also pretty similar to any other sample. Our estimate is going to be pretty close to the true population value. We would have a small confidence interval. But a more varied population will lead to a more varied sample. Different samples taken of the same population will differ more. We would b less sure that the sample mean was close to the population mean. Our confidence interval will be larger. So, greater variation in the population leads to a wider confidence interval.

**Sample size also affects the width of a confidence interval**

if we take a small sample we don’t have much information on which to base our inference. Small samples vary more from each other. in larger samples, the effect of a few unusual values is evened but by the other values in the sample. Larger samples will be more similar to each other. the effect of sampling error is reduced with larger samples. the confidence interval can be smaller.

#### Calculating Confidence Intervals

Various methods are available for calculating the confidence interval;

- Informal,
- Traditional Normal-based formulas and
- Bootstrapping.

##### Traditional Normal-based

When we use traditional confidence interval formulas, the stated level of confidence also effects the width of the confidence interval.

All estimates of a population parameter such as means, median, differences in means and differences in medians should be expressed as confidence intervals.

### Calculate Confidence Interval using our Confidence Interval Calculator

- Access Freepion SEO tools
- Access Confidence interval calculator
- Select or Enter values of sample mean, Sample size, Standard deviation and Confidence level
- After this, click on the button of calculate as shown below.
- Results appear that show the confidence level.