Summary

• When testing a claim in a hypothesis test, the three main components of the test are:
  1. assuming that the claim being tested is true at the beginning of the test
  2. using sampling distributions to work out what this assumption means for samples that may be collected
  3. collecting a sample and using it as evidence to test this assumption
• When conducting a hypothesis test, the claim being tested becomes a hypothesis in the test, the null hypothesis. The test begins by assuming that this hypothesis is true.
• Since the claim involves assigning a specific value to a population parameter, assuming this claim is true enables conclusions to be drawn about the sampling distribution of the parameter.
• In particular, a range of likely values for a sample statistic can be calculated.
• For example, assuming the claim that a population proportion π is equal to 0.5 may lead to the assertion that 95% of all sample proportions must lie between 0.451 and 0.549.
• A sample is then collected and a sample statistic is calculated, to test the assumption.
• If the sample statistic is not in the range of likely values, the assumption is rejected. That is, it is concluded that the claim in the null hypothesis is false.
• If the sample statistic is in the range of likely values, the assumption is not rejected.
• Hypothesis tests inherently involve some uncertainty, and errors can be made.
• For example, the assumed claim may be rejected even if it is in fact correct. This can happen if an unlikely sample is drawn.