Summary

• Hypothesis testing is one of the two major fields within statistical inference.
• We use hypothesis testing when a claim is made about a population parameter that can be tested.
• In particular, when a claim is made that a population parameter is equal to some specific value, this claim becomes a hypothesis to be tested.
• A sample is collected and, based on some measurements of the sample, we either:
  • reject the hypothesis that the proposed value for the population parameter is correct; or
  • not reject this hypothesis
• The claim that is tested is always that a population parameter (like a population mean or population proportion) takes some specific value. This claim is known as the null hypothesis, denoted H₀.

• For example, a null hypothesis would be that the population mean μ of a numerical variable is equal to 60:

  H₀: μ = 60

• The alternative hypothesis, denoted H_A, is a claim that the population parameter assumes some set of values other than the one assigned in the null hypothesis.

• The alternative hypothesis can be two-sided, which means that it only claims that the population parameter is not equal to the value specified in the null hypothesis:

  H_A: μ ≠ 60

• Or the alternative hypothesis can be one-sided, which means that it claims that the population parameter is specifically less than (or specifically greater than) the value specified in the null hypothesis:

  H_A: μ < 60

  or

  H_A: μ > 60

• At the end of the hypothesis test, either the null hypothesis is rejected (there is enough evidence to conclude that the specified value was wrong) or is not rejected (there is not enough evidence to conclude that the specified value was wrong).