Find the value of the $\chi ^ { 2 }$ test statistic for a hypothesis test of independence. Round your answer to 3 decimal places.
-Tests for adverse reactions to a new drug yielded the results given in the table. $\begin{array}{l|cc}
& \text { Drug } & \text { Placebo } \
\hline \text { Headaches } & 11 & 7 \
\text { No headaches } & 73 & 91
\end{array}$

A) $1.978$
B) $0.180$
C) $1.798$
D) $3.841$

Question

Find the value of the $\chi ^ { 2 }$ test statistic for a hypothesis test of independence. Round your answer to 3 decimal places.
-Tests for adverse reactions to a new drug yielded the results given in the table. $\begin{array}{l|cc} 
& \text { Drug } & \text { Placebo } \
\hline \text { Headaches } & 11 & 7 \
\text { No headaches } & 73 & 91
\end{array}$

A) $1.978$
B) $0.180$
C) $1.798$
D) $3.841$

Quizplus · Accepted Answer

The $\chi^2$ test statistic is calculated using the formula: $\chi^2 = \sum \frac{(O - E)^2}{E}$, where $O$ represents the observed frequencies and $E$ represents the expected frequencies under the null hypothesis of independence. The expected frequencies are calculated based on the marginal totals of the table. For this table, the expected frequencies are calculated as follows: $E_{11} = \frac{(11+7)(11+73)}{182}$, $E_{12} = \frac{(11+7)(7+91)}{182}$, $E_{21} = \frac{(73+91)(11+73)}{182}$, and $E_{22} = \frac{(73+91)(7+91)}{182}$. After calculating the expected frequencies, we apply them in the formula to get the $\chi^2$ value, which rounds to $1.798$.

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