# T-test

A t-test is a type of significance test that one conducts when the standard deviation of the population is unknown.

## Procedures

#### Step 1: State hypotheses

State the significance level and if the test is 1- or 2-sided.

#### Step 2: State assumptions

The assumptions are:

• The sample is normal
• The sample is an SRS

#### Step 3: Calculate stuff

$\text{Standard error}=s\sqrt{\dfrac1n}\sqrt{\dfrac{N-n}{N-1}}$ where the last radical can be ignored if $N>10n$ $\text{Test statistic}=\dfrac{\overline x-\mu}{\text{Standard error}}$ Degrees of freedom is n-1 P-value=tCdf(test statistic, $\infty$, degrees of freedom)

#### Step 4: State conclusion

If the P-value is less than the significance level, we say: There is sufficient sample evidence to reject the null(or something similar). If not, we say: There is insufficient sample evidence to reject the null(or something similar)