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Thursday, December 6, 2018

Central Limit Theorem and t-Distribution for Hypothesis Testing

Central Limit Theorem

The Central Limit Theorem state that as the sample size (i.i the number of values in each sample) gets large enough, the sampling distribution of the mean is approximately normally distributed. This is true regardless of the shape of the distribution of the individual values in the population.

Below statistic is used in testing of Hypothesis is σ is known.

Z-Score = (x̅ - μ)/(σ/sqrt(N))

x̅ is sample mean
μ is population mean
σ is population standard deviation
N is number of samples

t-Distribution & its Properties

if the random variable is normally distributed then t statistic value will follow t-distribution with (n-1) degrees of freedom and can be used for hypothesis testing.

t statistic = (x̅ - μ)/(S/sqrt(N))

x̅ is sample mean
μ is population mean
σ is sample standard deviation

N is number of samples

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