A software company wants to determine whether there is a relationship between their three sales offices and the sales of their software products. The actual sales results are :
$\begin{array}{lccc}
& \text { Product A } & \text { Product B } & \text { Product C } \
\text { Office 1 } & 17 & 10 & 23 \
\text { Office 2 } & 18 & 23 & 9 \
\text { Office } 3 & 26 & 10 & 64
\end{array}$
Under the null hypothesis, what is the expected amount of Product A that would be sold by Office 2 ?
A) 12.20
B) 15.25
C) 20.33
D) 30.50

Question

A software company wants to determine whether there is a relationship between their three sales offices and the sales of their software products. The actual sales results are : 
$\begin{array}{lccc} 
& \text { Product A } & \text { Product B } & \text { Product C } \
\text { Office 1 } & 17 & 10 & 23 \
\text { Office 2 } & 18 & 23 & 9 \
\text { Office } 3 & 26 & 10 & 64
\end{array}$
Under the null hypothesis, what is the expected amount of Product A that would be sold by Office 2 ?
A) 12.20
B) 15.25
C) 20.33
D) 30.50

Quizplus · Accepted Answer

To calculate the expected value, we need to assume there is no relationship between the sales offices and the sales of software products. We do this by calculating the row and column totals and using them to find the expected values.

The row and column totals are:

$\begin{array}{lccc|c} 
& \text { Product A } & \text { Product B } & \text { Product C } & \ \hline
\text { Office 1 } & 17 & 10 & 23 & 50 \
\text { Office 2 } & 18 & 23 & 9 & 50 \
\text { Office } 3 & 26 & 10 & 64 & 100 \ \hline
& 61 & 43 & 96 & \
\end{array}$

The expected value of Product A sold by Office 2 can be calculated as:

Expected value = (row total * column total) / overall total

Expected value of Product A sold by Office 2 = (50 * 61) / 200 = 15.25

Therefore, the answer is B.

A Software Company Wants to Determine Whether There Is a Relationship