Free Confidence Interval Calculator

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.

traditional FreePion

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

  1. Access Freepion SEO tools
  2. Access Confidence interval calculator
  3.  Select or Enter  values  of sample mean,  Sample size, Standard deviation and Confidence level
  4. After this, click on the button of calculate as shown below.
  5. 78 FreePion
  6. Results appear that show the confidence  level.