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Confidence Interval Formula

The Confidence Interval used in statistics to describe the amount of uncertainty associated with a sample estimate of a population parameter. It describes the uncertainty associated with a sampling method.

Confidence interval is a range within which most plausible values would occur. To calculate confidence interval, one needs to set confidence level as 90%, 95%, or 99% etc. A 90% confidence level means that we would expect 90% of the interval estimates to include the population parameter; 95% of the intervals would include the parameter and so on.

The formula for confidence interval is given below:
\[\large If\;n\geqslant 30,\;then\;Confidence\;Interval = x\pm z_{\frac{{\alpha}{2}}\left(\frac{\sigma }{\sqrt{n}} \right )\]
$and$
\[\large If\;n<30,\;then\;Confidence\;Interval = x\pm t_{\frac{\alpha}{2}}\left ( \frac{\sigma }{\sqrt{n}} \right )\]

Where,
n = Number of terms
x = Sample Mean
σ = Standard Deviation
$z_{\frac{\alpha }{2}}$ = Value corresponding to $\frac{\alpha }{2}$ in z table
$t_{\frac{\alpha }{2}}$ = Value corresponding to $\frac{\alpha }{2}$ in t table
$\alpha$ =1- $\frac{Confidence\;Level}{100}$.

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