Advanced Placement

Statistics and Probability

Chapter 13


Java Applets

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


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

    population is the same as the hypothesized amounts.

    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. 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 total.

    3. Use the same equation as Test for Goodness of Fit.

    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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