A study was recently done to examine the relationship between car color and the likelihood of being in an accident. The data is given in the table below.
$\begin{array}{c|ccc}
& \text { Red } & \text { Blue } & \text { White } \
\hline \text { Car has been in } & & & \
\text { accident } & 28 & 31 & 36 \
\text { Car has not been } & & & \
\text { in accidentt } & 24 & 22 & 30
\end{array}$
A) $\mathrm { H } _ { 0 }$ : The likelihood of being in an accident and car color are independent. $\mathrm { H } _ { \mathrm { a } }$ : The likelihood of being in an accident and car color are somehow related.
B) $\mathrm { H } _ { 0 }$ : The likelihood of being in an accident and car color are somehow related. $\mathrm { H } _ { \mathrm { a } }$ : The likelihood of being in an accident and car color are independent.
C) $\mathrm { H } _ { 0 }$ : The likelihood of being in an accident and car color are somehow related. $\mathrm { H } _ { \mathrm { a } }$ : The likelihood of being in an accident and car color are not independent.
D) $\mathrm { H } _ { 0 }$ : The likelihood of being in an accident and car color are independent. $\mathrm { H } _ { \mathrm { a } }$ : The likelihood of being in an accident and car color are not related.

Question

A study was recently done to examine the relationship between car color and the likelihood of being in an accident. The data is given in the table below. 
$\begin{array}{c|ccc} 
& \text { Red } & \text { Blue } & \text { White } \
\hline \text { Car has been in } & & & \
\text { accident } & 28 & 31 & 36 \
\text { Car has not been } & & & \
\text { in accidentt } & 24 & 22 & 30
\end{array}$
A) $\mathrm { H } _ { 0 }$ : The likelihood of being in an accident and car color are independent. $\mathrm { H } _ { \mathrm { a } }$ : The likelihood of being in an accident and car color are somehow related.
B) $\mathrm { H } _ { 0 }$ : The likelihood of being in an accident and car color are somehow related. $\mathrm { H } _ { \mathrm { a } }$ : The likelihood of being in an accident and car color are independent.
C) $\mathrm { H } _ { 0 }$ : The likelihood of being in an accident and car color are somehow related. $\mathrm { H } _ { \mathrm { a } }$ : The likelihood of being in an accident and car color are not independent.
D) $\mathrm { H } _ { 0 }$ : The likelihood of being in an accident and car color are independent. $\mathrm { H } _ { \mathrm { a } }$ : The likelihood of being in an accident and car color are not related.

Quizplus · Accepted Answer

In hypothesis testing, the null hypothesis ($H_0$) typically represents the default or no-effect assumption, in this case, that car color and accident likelihood are independent. The alternative hypothesis ($H_a$) suggests there is an effect or a relationship, meaning car color and accident likelihood are related.

A Study Was Recently Done to Examine the Relationship Between