C7 - Hypothesis Testing

• A hypothesis is a statement made about the value of a population parameter. A hypothesis test uses a sample or an experiment to determine whether or not to reject the hypothesis.
• The result of the experiment or the statistic that is calculated from the sample is called the test statistic.
• In order to carry out the test, you need to form two hypotheses:

  • the null hypothesis, H0, is the hypothesis that you assume to be correct
  • the alternative hypothesis, H1, tells you about the parameter if your assumption is shown to be wrong
• Hypothesis tests with alternative hypotheses in the form H1:p<… and H1:P>… are called one-tailed tests.
• Hypothesis tests with an alternative hypothesis in the form H1:p≠… are called two-tailed tests.
• To carry out a hypothesis test you assume the null hypothesis is true, then consider how likely the observed value of the test statistic was to occur. If this likelihood is less than a given threshold, called the significance level of the test, then you reject the null hypothesis.
• A critical region is a region of the probability distribution which, if the test statistic falls within it, would cause you to reject the null hypothesis.
• The critical value is the first value to fall inside of the critical region.
• The actual significance level of a hypothesis test is the probability of incorrectly rejecting the null hypothesis.
• For a two-tailed test the critical region is made up of two parts, one at each end of the distribution.
• For a two-tailed test the critical region is split at either end of the distribution.
• For a two-tailed test, either double the p-value for your observation, or halve the significance level at the end you are testing.
• The acceptance region is the area in which we accept the null hypothesis.