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Test statistic used in
a. one-mean $t-$test
b. one-mean $z-$test

The procedure is for:
Small sample size

• Samples are randomly selected.
• Population follows normal distribution or the sample size is larger.
• The standard deviation is unknown.

The test statistic for one-mean $t-$test is given below:

$t=\frac{\stackrel{炉}{x}-{渭}_0}{\frac{s}{\sqrt{n}}}$

The procedure is for:
Small sample size:
If the sample size is say less than $15$, the$z-$test procedure is used when the variable is normally distributed or very close to being normally distributed.
Moderate sample size:
If the sample size lies between $15-30$, the$z-$test procedure is used when the variable is far from being normally distributed or there is no outlier in the data.
Large sample size:
If the sample size is say greater than $30$, the$z-$test procedure is used without any restriction.
The test statistic for one-mean$z-$test is given below:
$z=\frac{\stackrel{炉}{x}-{渭}_0}{\frac{蟽}{\sqrt{n}}}$