Summary

• Statistical inference is an activity. Things like hypothesis tests are best understood by getting practice at conducting them.
• While a general step-by-step guide can always be used to indicate how to conduct a hypothesis test, doing examples of tests will expose the considerations that can arise for such tests.
• One such consideration is whether or not the population standard deviation σ is known when we are testing the population mean μ.
  • If σ is known, and we denote the proposed value for the population mean by μ₀, then:

    X - μ0

    σ/√n

    will follow the standard normal distribution.
  • If σ is not known, then:

    X - μ0

    S/√n

    will follow the t-distribution with n - 1 degrees of freedom.
• As a result, this will affect the critical values, region of rejection, and test statistic for the test.
• Another consideration in hypothesis testing is what to do when the test statistic is 'close' to the critical value.
• If the test statistic is not in the region of rejection, but is considered close to it, we still do not reject the null hypothesis. However, we may want to consider how strong the evidence against the null hypothesis is. This can be done by using the P-value method of hypothesis testing.