14 Chi-Square Procedures 14.2 Inference for Two-Way Tables

HW- pg. 856 (14.12) & pg. 866 (14.17) Chapter 14 Test Friday 4-19-13 AP REVIEW after School THURSDAY 4-25-13 www.westex.org HS, Teacher Website 4-16-13 Warm Up AP STATS Go over HW. Name ______Date ______AP Stats 14 Chi-Square Procedures 14.2 Inference for Two-Way Tables

The Chi-Square Test for Homogeneity of Populations Calculating the chi-square statistic (O  E) 2 X2 = Σ E The sum is over all r x c cells in the table.

The chi-square statistic from 14.1 is a ______of the chi-square statistic given here in which c = ___. Once X2 has been calculated, the difference between goodness of fit and homogeneity of populations procedures lies in the number of ______used to compute the P-value.

For goodness of fit, df = ______, where k is the number of categories.

In section 14.2, df = ______, where r is the number of rows and c is the number of columns in the two-way table.

The same chi-square procedure that we used to test goodness of fit allows us to compare distribution of proportions in several populations, (all expected counts greater than or equal to 5), provided that we take ______and ______random samples from each population.

Chi-Square Test for Homogeneity of Populations  Select independent _____ from each of c populations.  Classify each individual in a sample according to a categorical response variable with ___ possible values.  There are ___ different sets of proportions to be compared, one for each population.  The null hypothesis is that the distribution of the response variable is ______in all c populations. The alternative hypothesis is that these c distributions are not ______. 2 2  If Ho is true, the chi-square statistic X has approximately a X distribution with ______degrees of freedom.  The ______for the chi-square test is the area to the right of X2 under the chi-square density curve with (r – 1)(c – 1) DOF. The Chi-Square Test and the z Test Chi-square test is used to compare ______of proportions. If we have a 2 x 2 table the chi-square test is the same as the z test from 13.2. The chi-square statistic X2 is just the ______of the z statistic, and the P-value for X2 is exactly the same as the ______P-value for z. When comparing 2 proportions it is better to use the z Test because it gives you the choice of a ______test and is related to a

CI for p1 – p2.

14.16 How are schools doing? The nonprofit group Public Agenda conducted telephone interviews with 3 randomly selected groups of parents of high school children. There were 202 black parents, 202 Hispanic parents, and 201 white parents. One question asked was “Are the high schools in your state doing an excellent, good, fair, or poor job, or don’t you know enough to say?” Here are the survey results: Black parents Hispanic parents White parents Excellent 12 34 22 Good 69 55 81 Fair 75 61 60 Poor 24 24 24 Don’t know 22 28 14 TOTAL 202 202 201

Write a brief analysis of these results. Include a test of significance, and your own discussion of the most important findings.