*1. Give the critical 2 values and df for testing each of the following null hypotheses for one-variable problems at a ¼ :05 and a ¼ :01.

(a) H0 : p1 ¼ p2 ¼ p3 ¼ p4

(b) H0 : p1 ¼ :10, p2 ¼ :10, p3 ¼ :80

(c) H0 : p1 ¼ :25, p2 ¼ :75

(d) H0 : p1 ¼ p2

(e) H0 : p1 ¼ :50, p2 ¼ p3 ¼ p4 ¼ p5 ¼ p6 ¼ :10 frequency data versus score data chi-square one-variable case x2 goodness-of-fit test two-variable case x2 test of independence observed frequencies expected frequencies sampling distribution of x2 test of a single proportion confidence interval for p contingency table crosstabulation null hypothesis of independence expected frequencies in a contingency table test of independence testing a difference between two proportions the independence of observations quantitative variables Access the sophomores data file.