The following table shows the Myers-Briggs personality preferences for a random sample of 400 people in the listed professions. $$\begin{array} { l | l | l | l }
\text { Occupation } & \text { Extroverted } & \text { Introverted } & \text { Row Total } \
\hline \text { Clergy (all denominations) } & 63 & 42 & 105 \
\hline \text { M.D. } & 67 & 95 & 162 \
\hline \text { Lawyer } & 52 & 81 & 133 \
\hline \text { Column Total } & 182 & 218 & 400 \
\hline
\end{array}$$ Use the chi-square test to determine if the listed occupations and personality preferences are independent at . Find the value of the chi-square statistic for the sample.
$$\alpha = 0.01$$
A)12.22
B)0.01
C)12.01
D)0.22
E)9.20

Question

The following table shows the Myers-Briggs personality preferences for a random sample of 400 people in the listed professions. $$\begin{array} { l | l | l | l } 
\text { Occupation } & \text { Extroverted } & \text { Introverted } & \text { Row Total } \
\hline \text { Clergy (all denominations) } & 63 & 42 & 105 \
\hline \text { M.D. } & 67 & 95 & 162 \
\hline \text { Lawyer } & 52 & 81 & 133 \
\hline \text { Column Total } & 182 & 218 & 400 \
\hline
\end{array}$$ Use the chi-square test to determine if the listed occupations and personality preferences are independent at . Find the value of the chi-square statistic for the sample.
$$\alpha = 0.01$$
A)12.22
B)0.01
C)12.01
D)0.22
E)9.20

Quizplus · Accepted Answer

To calculate the chi-square statistic, we first need to find the expected frequencies for each cell under the assumption that occupation and personality preference are independent. The expected frequency for a cell is calculated as $(\text{Row Total} \times \text{Column Total}) / \text{Total}$.For Clergy (Extroverted), the expected frequency is $(105 \times 182) / 400 = 47.715$.For Clergy (Introverted), it's $(105 \times 218) / 400 = 57.285$.For M.D. (Extroverted), it's $(162 \times 182) / 400 = 73.71$.For M.D. (Introverted), it's $(162 \times 218) / 400 = 88.29$.For Lawyer (Extroverted), it's $(133 \times 182) / 400 = 60.575$.For Lawyer (Introverted), it's $(133 \times 218) / 400 = 72.425$.Next, we calculate the chi-square statistic using the formula $\chi^2 = \sum \frac{(O - E)^2}{E}$, where $O$ is the observed frequency and $E$ is the expected frequency.For Clergy (Extroverted), $\chi^2 = \frac{(63 - 47.715)^2}{47.715}$.For Clergy (Introverted), $\chi^2 = \frac{(42 - 57.285)^2}{57.285}$.For M.D. (Extroverted), $\chi^2 = \frac{(67 - 73.71)^2}{73.71}$.For M.D. (Introverted), $\chi^2 = \frac{(95 - 88.29)^2}{88.29}$.For Lawyer (Extroverted), $\chi^2 = \frac{(52 - 60.575)^2}{60.575}$.For Lawyer (Introverted), $\chi^2 = \frac{(81 - 72.425)^2}{72.425}$.Adding all these values together gives us the total chi-square statistic, which is approximately 12.22.

The Following Table Shows the Myers-Briggs Personality Preferences for a Random