A p-value (probability value) is a measure of statistics that describes the likelihood of an experiment’s results supporting the null hypothesis as opposed to the alternative hypothesis.

• Null Hypothesis: if a p-value supports the null hypothesis, then the observed results of an experiment are most likely due to random chance rather than a relevant pattern.

• Alternative Hypothesis: if a p-value rejects the null hypothesis, then it acts as supporting evidence for the alternative hypothesis, which is just the opposite of the null hypothesis.

• To find the p-value of a single-sampled test, we must first find the t-statistic, which observes variability in observed and hypothesized data. \[ t = \frac{\text{observed value} - \text{hypothesized value}}{\text{standard error}} \]
• Then, calculate degrees of freedom: \[ \text{DOF} = \text{sample size} - 1 \]
• After the t-test and DOF are found, a t-distribution table is used to find the p-value.

We use a significance value of \(\alpha = 0.05\). \[ p < 0.05 \quad \Rightarrow \quad \text{Reject Null Hypothesis } (H_0) \] Otherwise:

\[ p \geq 0.05 \quad \Rightarrow \quad \text{Failure to Reject Null Hypothesis } (H_0) \]