By Duane C. Hinders — McGrawHill Professional
Updated on Feb 4, 2011
Review the following concepts if necessary:
 ChiSquare GoodnessofFit Test for AP Statistics
 TwoWay Tables (Contingency Tables) Defined for AP Statistics
 Chisquare Test for Independence for AP Statistics
 ChiSquare Test for Homogeneity of Proportions (or Homogeneity of Populations) for AP Statistics
Problems
 Find the expected value of the cell marked with the "***" in the following 3 × 2 table (the bold face values are the marginal totals):
 74.60
 18.12
 12.88
 19.65
 18.70
 A Χ^{2} goodnessoffit test is performed on a random sample of 360 individuals to see if the number of birthdays each month is proportional to the number of days in the month. X^{2} is determined to be 23.5. The Pvalue for this test is
 0.001 < P < 0.005
 0.02 < P < 0.025
 0.025 < P < 0.05
 0.01 < P < 0.02
 0.05 < P < 0.10
 Two random samples, one of high school teachers and one of college teachers, are selected and each sample is asked about their job satisfaction. Which of the following are appropriate null and alternative hypotheses for this situation?
 H_{0}: The proportion of each level of job satisfaction is the same for high school teachers and college teachers.
 H_{0}: Teaching level and job satisfaction are independent.
 H_{0}: Teaching level and job satisfaction are related.
 H_{0}: The proportion of each level of job satisfaction is the same for high school teachers and college teachers.
 H_{0}: Teaching level and job satisfaction are independent.
H_{A}: The proportions of teachers highly satisfied with their jobs is higher for college teachers.
H_{A}: Teaching level and job satisfaction are not independent.
H_{A}: Teaching level and job satisfaction are not related.
H_{A}: Not all of the proportions of each level of job satisfaction are the same for high school teachers and college teachers.
H_{A}: Teaching level and job satisfaction are not related.
 A group separated into men and women are asked their preference toward certain types of television shows. The following table gives the results.
 The variables gender and program preference are independent.
 For these data, X^{2} = 0.
 The variables gender and program preference are related.
 I only
 I and II only
 II only
 III only
 II and III only
 For the following twoway table, compute the value of X^{2}.
 2.63
 1.22
 1.89
 2.04
 1.45
 The main difference between a Χ^{2} test for independence and a Χ^{2} test for homogeneity of proportions is which of the following?
 They are based on a different number of degrees of freedom.
 One of the tests is for a twosided alternative and the other is for a onesided alternative.
 In one case, two variables are compared within a single population. In the other case, two populations are compared in terms of a single variable.
 For a given value of X^{2}, they have different Pvalues.
 There are no differences between the tests. They measure exactly the same thing.
 A study is to be conducted to help determine if ethnicity is related to blood type. Ethnic groups are identified as White, AfricanAmerican, Asian, Latino, or Other. Blood types are A, B, O, and AB. How many degrees of freedom are there for a chisquare test of independence between Ethnicity and Blood Type?
 5 × 4 = 20
 5 × 3 = 15
 4 × 4 = 16
 5 + 4 – 2 = 7
 4 × 3 = 12
 Which of the following statements is (are) correct?
 A condition for using a Χ^{2} test is that most expected values must be at least 5 and that all must be at least 1.
 A Χ^{2} test for goodness of fit tests the degree to which a categorical variable has a specific distribution.
 Expected cell counts are computed in the same way for goodness of fit tests and tests of independence.
 I only
 II only
 I and II only
 II and III only
 I, II and III
Which of the following statements is (are) true?

1
 2
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From 5 Steps to a 5 AP Statistics. Copyright © 2010 by The McGrawHill Companies. All Rights Reserved.
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