Advanced Placement

Statistics and Probability

Chapter 13 Outline

Chapter 13

Main Topics


13.1 Test for Goodness of Fit

         A. Chi-Squared Distribution

              1. The Chi-Squared Distribution is skewed right.

              2. Must use Degreeā€™s of Freedom

              3. As the sample size increases, the curve

                  spreads out

         B. The test is to verify whether or not a distribution

              of a population is the same as the hypothesized


              1. The Null Hypothesis

                  a. The actual proportions is equal to the

                      hypothesized proportions

              2. Alternative Hypothesis

                  a. The actual proportions is different from the

                      hypothesized proportions

             3. Equation

                 a. (see Chi-Squared Eqn)

             4. Conditions

                 a. All expected counts are at least 1 or above

                 b. No more than 20% of the expected counts

                     are less than five

13.2 Inference for Two-Way Tables

        A. Two-Way Tables

            1. Dimensions are r x c (row and column)

            2. Expected counts are calculated by product of

                row total and column total divided by the entire


            3. Use the same equation as Test for Goodness of


            4. Degree of Freedom is calculated by (r-1)(c-1).

       B. Test for Homogeneity of Populations

            1. Test is reveal if the proportions for each group

                are the same.

       C. Test for Independence.

            1. Same test as Homogeneity, but the result is to

                determine if one category influences another






AP Statistics


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