AP Statistics Section 14.2 B

We can use the chi-square test of association/independence to test the null hypothesis

when you have a two-way table from a single SRS, with each individual classified according to both of two categorical variables.

variableslcatagorica twoebetween thn associatio no is There:0H

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.

Grade < 2 2 to 12 >12

C or better 11 68 3

D or F 9 23 5

per week) (hours

Activitiescular Extracurri

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

375.8

3 747.

91

68 55.

20

11

course. in thisbetter perform toseemper week hours

12 to2 activitescular extracurriin involved Students

b) Carry out an appropriate significance test.

Hypothesis:

The population of interest is _____________________________________________

H0: __________________________________________

Ha: __________________________________________

major eng. chem. afor required course ain NCSUat students

grade and E.A.on spent timeof amt. ebetween th iprelationsh no is There

grade and E.A.on spent timeof amt. ebetween th iprelationsh a is There

Conditions:

.population the

togeneralizenot may results SRS,an not If unknown. SRS

5.an greater th are counts

expectedother All 2.49.only is which R2C3 is

smallest The 1.least at are counts expected All

t.replacemen w/osampling since10n N

as long as ceindependen assume toreasonable Seems

Calculations:

926.6782.13

)782.1311( 22

926.6

.031 value-p

Conclusions:

course. in the grade the

and activitiescular extracurrion spent timeofamount ebetween th

iprelationsh a is e that therconclude and H reject the weso .05

of level cesignificancommon than theless is .031 of value-pOur

0

c) 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?

. variableslurking bemay There

causation.not but n associatio showmay study a ,NO