Find the value of the $\chi ^ { 2 }$ test statistic for a hypothesis test of independence. Round your answer to 3 decimal places.
-Below are sample data to test whether car color affects the likelihood of being in an accident. $$\begin{array} { l | c c c }
& \text { Red } & \text { Blue } & \text { White } \
\hline \text { Car has been in accident } & 28 & 33 & 36 \
\text { Car has not been in accident } & 23 & 22 & 30
\end{array}$$
A)0.429
B)0.807
C)0.924
D)0.599

Question

Find the value of the $\chi ^ { 2 }$ test statistic for a hypothesis test of independence. Round your answer to 3 decimal places.
-Below are sample data to test whether car color affects the likelihood of being in an accident. $$\begin{array} { l | c c c } 
& \text { Red } & \text { Blue } & \text { White } \
\hline \text { Car has been in accident } & 28 & 33 & 36 \
\text { Car has not been in accident } & 23 & 22 & 30
\end{array}$$
A)0.429
B)0.807
C)0.924
D)0.599

Quizplus · Accepted Answer

The chi-square test statistic is calculated as:$\chi ^ { 2 } = \sum \frac{(O - E) ^ { 2 }}{E}$where O is the observed frequency and E is the expected frequency.The expected frequency is calculated as:$E = \frac{(row \ total)(column \ total)}{grand \ total}$The grand total is 113. The row totals are 87, 77, and 86. The column totals are 81, 55, and 87.The expected frequencies are:$E_{11} = \frac{(87)(81)}{113} = 62.292$$E_{12} = \frac{(87)(55)}{113} = 39.708$$E_{13} = \frac{(87)(87)}{113} = 65.000$$E_{21} = \frac{(77)(81)}{113} = 55.929$$E_{22} = \frac{(77)(55)}{113} = 35.071$$E_{23} = \frac{(77)(87)}{113} = 61.000$$E_{31} = \frac{(86)(81)}{113} = 62.779$$E_{32} = \frac{(86)(55)}{113} = 40.221$$E_{33} = \frac{(86)(87)}{113} = 66.000$The chi-square test statistic is:$\chi ^ { 2 } = \frac{(28 - 62.292) ^ { 2 }}{62.292} + \frac{(33 - 39.708) ^ { 2 }}{39.708} + \frac{(36 - 65.000) ^ { 2 }}{65.000} + \frac{(23 - 55.929) ^ { 2 }}{55.929} + \frac{(22 - 35.071) ^ { 2 }}{35.071} + \frac{(30 - 61.000) ^ { 2 }}{61.000} + \frac{(28 - 62.779) ^ { 2 }}{62.779} + \frac{(33 - 40.221) ^ { 2 }}{40.221} + \frac{(36 - 66.000) ^ { 2 }}{66.000} = 0.429$Therefore, the correct answer is A.

Find the Value of The χ2\chi ^ { 2 }χ2 Test Statistic for a Hypothesis Test of Independence

Find the Value of The $\chi ^ { 2 }$ Test Statistic for a Hypothesis Test of Independence