The 1-Sample t conducts a hypothesis test of the mean based on sampled data when the population standard deviation, s is unknown. It also calculates a confidence interval of the mean. This procedure is based on the t-distribution which is derived from a normal distribution. It is more conservative than the Z-test for smaller sample sizes or when s is unknown.
|Test||Null Hypothesis, H0||Alternate Hypothesis, H1|
|One-tailed||μ = μ0||μ < μ0 or μ > μ0|
|Two-tailed||μ = μ0||μ ≠ μ0|
where μ is the population mean and μ0 is the hypothesised population mean