AP Statistics Chapter 11 Summary

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AP Statistics Chapter 11 Summary Chi-square Goodness of Fit Test What is it for? - 1 sample (1 population) - 1 variable with 2+ categories - Used to test whether the observed (sample) distribution is significantly different than the expected (claimed population) distribution. o Does the color distribution of milk chocolate means differ from what is claimed? o Distribution - Lower df -> more right-skewed - Higher df -> closer to normal - X^2 >= 0 - Hypothesis - Ho: P1=P2=P3=P4… =1/6 - Ha: At least 2 of the proportions of … are different (same every time) Conditions - Random sample / assignment - Independence N>=10n - All expected counts (np) >=5 Test Statistic - X^2 = sum (O-E) ^2 / E
- Df = k-1 o K = kategories - P (x^2 >= x^2) o Right tail probability o X^2 GOF Test on calculator o Follow-up Analysis - Determine which components (categories) contribute most to x^2 when rejecting Ho. - Find the largest differences. - Components are given when you run x^2 GOF test. Chi-squared test for Homogeneity Two-way Tables - Organizes data for categorical data into rows and columns. - Dimensions r x c and has r© elements. - What is it for? - Used to determine if multiple distributions are different across categories. o Multiple populations o 1 categorical variable
o Hypotheses - Ho: the distributions are the same across categories (in context) - Ha: the distributions are different across categories (in context) Conditions - Random sampling / assignment - Independence for random sampling without replacement (check for each population) - Expected counts >=5 o (row total) (column total) / n o Test Statistic - X^2 = sum (O-E) ^2 / E - Df = (r-1) (c-1) - X^2 test on calculator
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