A Study Was Recently Done to Examine the Relationship Between

question 41

Multiple Choice

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.

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Definitions:

Main Effect

In an experimental design, the direct impact of an independent variable on a dependent variable, disregarding the effects of other variables.

Simple Effect

The effect of one independent variable at a particular level of another independent variable in the context of more complex experimental designs.

Interaction Effect

The combined effect of two or more independent variables on a dependent variable that is different from the effect of each variable taken individually.

Main Effect

The impact of an independent variable on a dependent variable in an experimental design, disregarding the effects of other variables.