Summary
Highlights
Hypothesis testing involves making an assumption about a population and then using sample data to assess the plausibility of that assumption. The ultimate goal is to understand something about the overall population by testing an initial assumption using information from a sample.
The general process for solving any hypothesis test involves five steps: Create your hypotheses, Check conditions, Calculate your test statistic and P-value, Compare these values to a threshold, and Conclude based on your findings.
This step involves formulating two hypotheses: the null hypothesis (H₀), which represents the assumed state or status quo, and the alternative hypothesis (Hₐ), which is what you want to test or prove. A common strategy is to first write the alternative hypothesis based on what you suspect, and then the null hypothesis is its opposite. The null hypothesis always includes some form of an equal sign.
Before proceeding, specific conditions for each test type must be met to ensure the sample data accurately represents the population. After confirming conditions, it's helpful to draw a distribution (e.g., normal, t, F, chi-square) centered around the assumed population parameter from the null hypothesis, and then plot the sample statistic.
The sample statistic is converted into a standardized test statistic (e.g., Z, T, F, chi-square) to simplify calculations. This test statistic is then used to calculate the P-value, which is the probability of observing sample data as extreme or more extreme than what was collected, assuming the null hypothesis is true. The direction of shading for the P-value is determined by the alternative hypothesis.
The P-value is compared to an alpha (α) value (significance level), or the test statistic is compared to a critical value. If the P-value is less than alpha ('if p is low, reject H₀'), or the absolute value of the test statistic is greater than the absolute value of the critical value, the null hypothesis is rejected in favor of the alternative hypothesis. Conversely, if the P-value is greater than alpha, or the test statistic is not beyond the critical value, you fail to reject the null hypothesis, meaning there isn't enough evidence to support the alternative.