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# ${ \chi}^{2}$ Independence: How Much Freedom In Relationships?

APSTAT-6KNX0J

A student wondered if there was an association between relationship status and overall letter grade(based off grade point average) at her high school. She used a stratified random sample to select 20 students within each letter grade. The information is displayed in the table below.

Letter Grade In a relationship Not in a relationship Total
A 8 12 20
B 11 9 20
C 13 7 20
D 10 10 20
F 6 14 20
Total 48 52 100

Which of the following is the number of degrees of freedom used for the appropriate test of significance?

A

$2$

B

$4$

C

$5$

D

$10$

E

$18$