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${ \chi}^{2}$ Independence: Relationships or Grades?

APSTAT-VRH8JL

A student wondered if there was an association between relationship status and overall letter grade(based on 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



A ${ \chi}^{2}$ test of independence was conducted to determine whether the data above provides convincing evidence of an association between relationship status and overall letter grade. The ${ \chi}^{2}$ test statistic was $5.849$ with a $p$-value of $0.211$. Which of the following statements is true?

A

No relevant conclusion can be made because the data is not normally distributed.

B

Since the $P$-value is greater than the significance level of $\alpha =0.05$, their is sufficient evidence to suggest relationship status and overall letter grade are independent.

C

Since the $P$-value is greater than the significance level of $\alpha =0.05$, their is sufficient evidence to suggest relationship status and overall letter grade are dependent.

D

Since the $P$-value is greater than the significance level of $\alpha =0.05$, their is insufficient evidence to suggest an association between relationship status and overall letter grade.

E

Since the $P$-value is greater than the significance level of $\alpha =0.05$, their is sufficient evidence to suggest an association between relationship status and overall letter grade.