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AP Statistics Chapter 11 Flashcards

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13329338618chi-square goodness of fit testtests the H0 that a categorical variable has a specified distribution in the population point of interest one way table0
13329352289observed countsActual numbers of individuals in the sample that fall in each cell of the one-way or two-way table.1
13329357672expected countsNumber of individuals in the sample that would fall in each cell of the table if null were true (find by multiplying sample size by proportion of each category according to the H0)2
13329369015chi square statistica measure of how far the observed counts are from the expected counts3
13329374595chi square distributiondensity curve that has only nonnegative values and skewed right. Chi-square distribution is specified by giving degrees of freedom. The chi-square test for goodness of fit uses the chi-square distribution with degrees of freedom = the number of categories −1 Mean of a particular chi-square distribution = to its degrees of freedom. For df > 2, the mode (peak) of the chi-square density curve is at df − 2. become more "normal" looking as df increases4
13329394299conditions for performing a chi square goodness of fit testRandom: The data come from a well-designed random sample or randomized experiment 10%: When sampling without replacement, check that n0.10N Large counts: All expected counts≥5.5
13329404193hypotheses for goodness of fitH0: The stated distribution of the categorical variable in the population of interest is correct. Ha: at least one of The stated distribution of the categorical variable in the population of interest is not correct.6
13329414362find p value using chi square curvechi square cdf lb: chi^2 value ub:1E99 df: categories-1 (goodness of fit) or # rows-1 x # columns-1 (homogeneity or independent)7
13329453043performing chi square goodness of fit test calculatorstat, test, x^2 GOF test (D) gives x^2. df, contribution to x^2 2nd distr, x^2 cdf8
13329473762chi square test for homogeneitytest to determine whether the distribution of a categorical variable is the same for each of several populations or treatments9
13329488233chi square test for homogeneity hypothesesH0: There's no difference in distribution of a categorical variable for several pops or treatments Ha: There's a difference in distribution of a categorical variable for several pops or treatments10
13329497013chi square for independencetest to determine whether there is convincing evidence of an association between the row and the column variables in a 2-way table COMES FROM SINGLE SAMPLE11
13329504588chi-square test for independence hypothesesH0: There is no association between two categorical variables in the population of interest. Ha: There is an association between two categorical variables in the population of interest. or H0: Two categorical variables are independent in the population of interest. Ha: Two categorical variables are not independent in the population of interest.12
13329521212find expected counts for homogeneity and Independencewhen H0 is true13
13329597687finding degrees of freedom for chi square14
13329539592conditions for performing a chi square for homogeneity or independenceRandom: The data come from a well-designed random sample or randomized experiment 10%: When sampling without replacement, check that n0.10N Large counts: All expected counts≥5.15
13329552724difference between homogeneity and IndependenceHomogeneity tests whether the distribution of a categorical variable is the same for each of several populations or treatments. Independence tests whether two categorical variables are associated in some population of interest. If data come from 2+ independent random samples or treatment groups in a randomized experiment, then do homogeneity. If the data come from a SRS, with individuals classified according to two categorical variables, use independence.16
13329566388Interpreting P-Valueif the true mean/proportion of the population is (null), the probability of getting a sample mean/proportion of _____ is (p-value) by chance alone. assuming H0, there is a p value probability of observing ... by change alone17

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