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Confidence Interval Calculator
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Confidence Interval Calculator is used to calculate the confidence limits for mean with respect to the given values of sample size, standard deviation, mean and confidence level.

Confidence Interval Formula

If(n $\geq$ 30)
Confidence Interval = x $\pm$ z$_{\frac{\alpha}{2}}$ $\times$ $\left(\frac{\sigma}{\sqrt{n}}\right)$
If(n < 30)
Confidence Interval = x $\pm$ t$_{\frac{\alpha}{2}}$ $\times$ $\left(\frac{\sigma}{\sqrt{n}}\right)$
Where,
x = Sample Mean
$\sigma$ = Standard Deviation
$\alpha$ = 1 - $\left(\frac{Confidence\ Level}{100}\right)$
Z$_{\frac{\alpha}{2}}$ = Value of the z-table
t$_{\frac{\alpha}{2}}$ = Value of the t-table.

You can see a default confidence level, sample size, standard deviation, mean given below. Click on "Calculate". Confidence interval is calculated by applying the default values in the confidence interval formula.
 

How to Calculate Confidence Interval

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Step 1 :  

Observe the value of given mean and standard deviation for a respective sample size to find the confidence interval at a particular confidence level for mean percent.



Step 2 :  

Apply the Confidence Interval Formula:


If(n $\geq$ 30)
Confidence Interval = x $\pm$ z$_{\frac{\alpha}{2}}$ $\times$ $\left(\frac{\sigma}{\sqrt{n}}\right)$
If(n < 30)
Confidence Interval = x $\pm$ t$_{\frac{\alpha}{2}}$ $\times$ $\left(\frac{\sigma}{\sqrt{n}}\right)$
Where,
x = Sample Mean
$\sigma$ = Standard Deviation
$\alpha$ = 1 - $\left(\frac{Confidence\ Level}{100}\right)$
Z$_{\frac{\alpha}{2}}$ = Value of the z-table
t$_{\frac{\alpha}{2}}$ = Value of the t-table.



Confidence Interval Example

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  1. In a survey of 20 persons to find what percent of their income is given to charity, discover mean percent is 16 with a standard deviation of 6 percent. Find the confidence interval of mean percent at 95%?


    Step 1 :  

    Given Sample size = 20 persons


    Sample mean = 16


    Standard deviation = 6


    Confidence interval of mean percent = 95% = 0.95



    Step 2 :  

    Since n < 30, So
    Confidence Interval = x $\pm$ t$_{\frac{\alpha}{2}}$ $\times$ $\left(\frac{\sigma}{\sqrt{n}}\right)$
    Confidence Interval = 16 $\pm$ t$_{\frac{0.05}{2}}$ $\times$ $\left(\frac{6}{\sqrt{20}}\right)$
    Confidence Interval = 16 $\pm$ 2.09302 $\times$ $\left(\frac{6}{\sqrt{20}}\right)$


    So, the margin of error = $\pm$ 2.808


    95% confidence interval from 13.1919 to 18.8081



    Answer  :  

    95% confidence interval from 13.1919 to 18.8081



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