The Big Picture
          Probability
           Statistical inference always involves an argument based on probability.
           Recall the following important points about probability
           •  Probability is a measure of how likely an event is to occur.
           •  We can make probability statements only about random 
              events. Random here means that the outcome is uncertain in the short 
              run but has a predictable pattern in the long run.
   Inference
            Research Questions That Involve Inference
                Type of Question             Examples                      Variable Type                 Unit
                Make an estimate about  What proportion of all U.S.        Categorical variable          Inference for One 
                the population               adults support the death                                    Proportion
                                             penalty?
                Make an estimate about  What is the average                Quantitative variable         Inference for Means
                the population               number of hours that 
                                             community college 
                                             students work each week?
                Test a claim about the       Do the majority of            Categorical variable          Inference for One 
                population                   community college                                           Proportion
                                             students qualify for federal 
                                             student loans?
                Test a claim about the       Has the average birth         Quantitative variable         Inference for Means
                population                   weight in a town decreased 
                                             from 3,500 grams?
                Compare two                  Are teenage girls more        Categorical variable          Inference for Two 
                populations                  likely to suffer from                                       Proportions
                                             depression than teenage 
                                             boys?
                Compare two                  In community colleges do      Quantitative variable         Inference for Means
                populations                  female students have a 
                                             higher average GPA than 
                                             male students?
          Inference Procedure
           Each research question from the previous slide relates to either a 
           categorical variable or a quantitative variable. In this course, three criteria 
           determine the inference procedure we use:
           •  The type of variable.
           •  The type of inference (estimate a population value or test a claim about a 
              population value).
           •  The number of populations involved.