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**AP Statistics Section 14.2 B **

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We can use the chi-square test of association/independence to test the null hypothesis “ There is ____ association between the two categorical variables.” when you have a two-way table from a single SRS, with each individual classified according to both of two categorical variables.

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Example: North Carolina State University studied student performance in a course required for its chemical engineering major. One question of interest is the relationship between time spent in extracurricular activities and whether a student earned a C or better in the course. Here are the data for 119 students who answered a question about extracurricular activities.

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Grade < 2 2 to 12 >12 C or better 11 68 3 D or F 9 23 5

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a) Find the proportion of students (C or better) in each of the three extracurricular activity groups. What do these proportions show?

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**b) Carry out an appropriate significance test**

b) Carry out an appropriate significance test. Hypothesis: The population of interest is _____________________________________________ H0: __________________________________________ Ha: __________________________________________

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Conditions:

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Calculations:

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Conclusions:

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**c) Which term(s) contribute the most to**

c) Which term(s) contribute the most to ? What does this show you about the relationship between the time spent in extracurricular activities and academic performance in this particular course?

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d) Does the study convince you that there is a relationship between the amount of time spent in extracurricular activities and academic performance in this course?

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Comparing Observed Distributions A test comparing the distribution of counts for two or more groups on the same categorical variable is called a chi-square.

Comparing Observed Distributions A test comparing the distribution of counts for two or more groups on the same categorical variable is called a chi-square.

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