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The One Sample t-Test is a hypothesis test used to test the mean of a small sample taken from a population with a normal distribution against a specified value. The hypothesis is:
H0 the population mean equals a specified value
H1 the popular mean is [equal to/less than/greater than] a specified value
The test is:
where:
 |
sample mean |
| μ 0 |
specified value |
| s |
sample standard deviation |
| n |
sample size |
The critical value of the t statistic t0 can be found in t distribution tables, or the p-value can be found using the Excel function:
=TDIST(|t0|, ν , Tails)
The number of degrees of freedom 'ν ' is n - 1, the number of tails is 1 for a one sided test and 2 for a two sided test.
The t-test requires that the population conforms to a normal distribution.
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