Confidence Interval Calculator

Confidence Interval Calculator 

Confidence calculator helps if we know the sample size, standard deviation, and mean, you can use this calculator to get the confidence interval for your sample. There is no hard and fast rule for how much faith you should have in using it. 
This article will be useful if you have ever wondered what a confidence interval is, how to construct one, or if you want to know how to generate a 95% confidence interval with no margin of error.

What is CI?

Confidence intervals are defined as "the range of values, calculated from sample statistics that are likely to include the value of an unknown population parameter." However, what does that actually imply? Yes, a confidence calculator makes it possible, if you have parameters values of your sample size. 
Have a look at this example for better understanding.  Just imagine a brick manufacturer who is not sure if the volume of bricks he's producing is acceptable. The bulk of a sample of one hundred bricks, according to his measurements, is three kilograms. Its 95% confidence interval, which he has also calculated, is 3.85 kg 4.15 kg. This suggests that he can produce bricks with an average mass of between 3.85 kg and 4.15 kg, with a 95% confidence interval.

One particular inquiry that piques economists' curiosity is this: "How does a variation in the interest rate influence the price level?" The actual population mean will fall within around 95% of the confidence intervals calculated by drawing samples from the population over and over again and using the results to calculate a set of confidence intervals. Only 5% of the interval will accurately represent the population mean.

Features of confidence interval calculator 

CI calculator is associated with the moment-based estimation technique. The sample mean is a good approximation of the population mean, for example, which is a simple quantity to estimate. The variance in the sample can also be used to estimate the variation in the whole population. With the sample mean as its center, a confidence interval for the real mean can be built with a width equal to some multiple of the square root of the sample variance.

Likelihood formula

The confidence interval calculator will calculate the likelihood value of CI by using the maximum likelihood principle that gives two methods for creating confidence intervals or confidence regions for constructing estimates.

Formulas for approximation

The here-applied method of estimate can be thought of as a generalization of both the moment approach and the maximum probability technique. The CI calculator will calculate maximum likelihood theory's findings and can be generalized in ways that make it possible to create confidence intervals using estimates obtained via estimating equations. 

Verifying Hypotheses

The CI calculator also does testing of hypotheses. Using hypothesis tests for all possible parameter values, one may generate confidence intervals/regions by including all points for which the null hypothesis that the true value is the given value is not refuted at a significance level of (1 p) inside the 100 p% confidence region.

Bootstrapping

Confidence intervals and prediction intervals can be constructed in CI calculators by using resampling methods when the distributional assumptions underlying the aforementioned approaches are unknown or violated. Then we can easily infer the population-level correlations from the observed distribution of data and the internal correlations.

How to calculate confidence interval

The components required to compute a CI on calculate you must need the values of these parameters:

AVG, S.D and n= You need to know your average, standard deviation and sample size n that you can put in CI calculator
If you do not know how to calculate average, s.d and n, then no need to worry, simply put all values that you have, CI calculator will calculate all these parameters. 

Confidence level; You must have certainty level that you put all true values of raw data  

Population standard deviation= put S.D value that is necessary to compute confidence interval mean calculator but  if you do not know what is your population standard deviation value CI calculator will find it out. 

Mean confidence interval calculator 

The CI calculator will find out mean for a given confidence interval by applying the normal distribution if and only if we know the standard deviation () of the population. The mean (Mean, /n) has a normal distribution across x. Otherwise, the t distribution with n-1 degrees of freedom and the sample size's standard deviation should be used. The distribution of 
-(x-Mean)/(S/n) is t.

Formula of mean to find CI

When we know the standard deviation of the population: 
x̄ ± Zα/2 * σ √n
When we can utilize the standard deviation because we don't have information on the population's standard deviation as below: 
T/2(df) * Sn where x is a constant.

Confidence interval calculator is important

It's crucial because, in most cases, you can't collect information from everyone in a population. Therefore, we use the data we have to estimate the population proportion, taking the potential margin of error into account. We may calculate a range using this error margin. A confidence interval describes this interval.

 A confidence interval can be used to convey how accurately the data sample represents the entire population. As long as it's less than 100%, you can find a confidence interval. However, the most representative interval size is 95%.

If one were to compute the confidence interval for an unlimited sample size, then 95% of the estimated ranges would include the population parameter, which is the basis of the 95% confidence interval. 

How to calculate confidence interval 

The confidence interval is calculated by using this formula
Best estimator ± Margin of error
Margin of error= z*S.E
In most cases, we prioritize a high degree of certainty such as 95%, 99%, or 75% which means the greater the confidence level (CL), the less accurate the results will be. In the preceding scenario, an estimate of 85% is considered to be most accurate. Using the following formula, we can determine the SE of our estimates:

Standard of error

S.E=  √ (p (1-p1)/ n
Where n is given sample size  and p is the best estimator of the population mean