The following table shows the Myers-Briggs personality preferences for a random sample of 409 people in the listed professions. $$\begin{array} { l | l | l | l }
\text { Occupation } & \text { Extroverted } & \text { Introverted } & \text { Row Total } \
\hline \text { Clergy (all denominations) } & 62 & 44 & 106 \
\hline \text { M.D. } & 70 & 94 & 164 \
\hline \text { Lawyer } & 54 & 85 & 139 \
\hline \text { Column Total } & 186 & 223 & 409 \
\hline
\end{array}$$ Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.1 level of significance. What are the degrees of freedom?
A)4
B)3
C)2
D)5
E)6

Question

The following table shows the Myers-Briggs personality preferences for a random sample of 409 people in the listed professions. $$\begin{array} { l | l | l | l } 
\text { Occupation } & \text { Extroverted } & \text { Introverted } & \text { Row Total } \
\hline \text { Clergy (all denominations) } & 62 & 44 & 106 \
\hline \text { M.D. } & 70 & 94 & 164 \
\hline \text { Lawyer } & 54 & 85 & 139 \
\hline \text { Column Total } & 186 & 223 & 409 \
\hline
\end{array}$$ Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.1 level of significance. What are the degrees of freedom?
A)4
B)3
C)2
D)5
E)6

Quizplus · Accepted Answer

The degrees of freedom for a chi-square test of independence are calculated as (number of rows - 1) * (number of columns - 1). Here, we have 3 occupations (rows) and 2 personality preferences (columns), so the degrees of freedom are (3-1)*(2-1) = 2*1 = 2.

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