The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in the listed professions. Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.1 level of significance. Depending on the P-value, will you reject or fail to reject the null hypothesis of independence?
$$\begin{array} { l | l | l | l }
\text { Occupation } & \text { Extroverted } & \text { Introverted } & \text { Row Total } \
\hline \text { Clergy (all denominations) } & 62 & 44 & 106 \
\hline \text { M.D. } & 66 & 94 & 160 \
\hline \text { Lawyer } & 56 & 84 & 140 \
\hline \text { Column Total } & 184 & 222 & 406 \
\hline
\end{array}$$
A)Since the P-value is greater than $\alpha$, we fail to reject the null hypothesis that the Myers-Briggs personality preference and profession are not independent. At 0.1 level of significance, we conclude that the Myers-Briggs personality preference and profession are independent.
B)Since the P-value is greater than $\alpha$, we reject the null hypothesis that the Myers-Briggs personality preference and profession are not independent. At 0.1 level of significance, we conclude that the Myers-Briggs personality preference and profession are independent.
C)Since the P-value is less than $\alpha$, we reject the null hypothesis that the Myers-Briggs personality preference and profession are not independent. At 0.1 level of significance, we conclude that the Myers-Briggs personality preference and profession are independent.
D)Since the P-value is less than $\alpha$, we reject the null hypothesis that the Myers-Briggs personality preference and profession are independent. At 0.1 level of significance, we conclude that the Myers-Briggs personality preference and profession are not independent.
E)Since the P-value is less than $\alpha$, we fail to reject the null hypothesis that the Myers-Briggs personality preference and profession are independent. At 0.1 level of significance, we conclude that the Myers-Briggs personality preference and profession are not independent.

Question

The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in the listed professions. Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.1 level of significance. Depending on the P-value, will you reject or fail to reject the null hypothesis of independence?
$$\begin{array} { l | l | l | l } 
\text { Occupation } & \text { Extroverted } & \text { Introverted } & \text { Row Total } \
\hline \text { Clergy (all denominations) } & 62 & 44 & 106 \
\hline \text { M.D. } & 66 & 94 & 160 \
\hline \text { Lawyer } & 56 & 84 & 140 \
\hline \text { Column Total } & 184 & 222 & 406 \
\hline
\end{array}$$
A)Since the P-value is greater than $\alpha$, we fail to reject the null hypothesis that the Myers-Briggs personality preference and profession are not independent. At 0.1 level of significance, we conclude that the Myers-Briggs personality preference and profession are independent.
B)Since the P-value is greater than $\alpha$, we reject the null hypothesis that the Myers-Briggs personality preference and profession are not independent. At 0.1 level of significance, we conclude that the Myers-Briggs personality preference and profession are independent.
C)Since the P-value is less than $\alpha$, we reject the null hypothesis that the Myers-Briggs personality preference and profession are not independent. At 0.1 level of significance, we conclude that the Myers-Briggs personality preference and profession are independent.
D)Since the P-value is less than $\alpha$, we reject the null hypothesis that the Myers-Briggs personality preference and profession are independent. At 0.1 level of significance, we conclude that the Myers-Briggs personality preference and profession are not independent.
E)Since the P-value is less than $\alpha$, we fail to reject the null hypothesis that the Myers-Briggs personality preference and profession are independent. At 0.1 level of significance, we conclude that the Myers-Briggs personality preference and profession are not independent.

Quizplus · Accepted Answer

If the P-value is less than the level of significance (0.1 in this case), it indicates that the observed data are unlikely under the null hypothesis of independence. Therefore, we reject the null hypothesis, suggesting that there is a significant association between Myers-Briggs personality preference and profession.

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