The human resources department of a large finance company is attempting
to determine if an employee’s performance is influenced by their undergraduate degree subject.
The 5 subjects considered are: Marketing, Marketing & Management,
Business Management, Accounting & Finance and
.
Personnel ratings are grouped as Excellent, Strong and
Average.
A recent assessment gave the following results:
\begin{tabular}{r|rrr|r}
& \textbf{Excellent} & \textbf{Strong} & \textbf{Average} & \textbf{Totals}\\
\hline\textbf{Marketing} & 15 & 26 & 11& 52 \\
\textbf{Marketing Management} & 26& 25& 21 &72 \\
\textbf{Business Management} &10 &12 &13 &35 \\
\textbf{Accounting Finance} &18 &14& 13 &45 \\
\textbf{Mathematics} &21 &14 &10& 45 \\
\hline\textbf{Totals} &90 &91 &68 &249
\end{tabluar}
Test the null hypothesis that there is no association between degree subject and performance.
a)
Step 1: Null hypothesis
H_0: There is no association between degree subject and performance.
Step 2: Alternate hypothesis
H_1: There is an association between degree subject and performance.
b)
Step 3: Test statistic
You are given the expected frequencies (all to 3 decimal places) for Marketing, Marketing & Management and Accounting & Finance.
You have to calculate the expected frequencies for Business Management and Mathematics and put them in the following table.
Input each expected frequency to 3 decimal places.
\begin{tabular}{r|rrr|r}
\textbf{EXPECTED FREQUENCIES} & \textbf{Excellent} & \textbf{Strong} & \textbf{Average}\\
\hline\textbf{Marketing} & 18.795 & 19.004 & 14.201 \\
\textbf{Marketing Management} & 26.024& 26.313& 19.663 \\
\textbf{Business Management& \input & \input & \input \\
\textbf{Accounting Finance}& 16.265 &16.446& 12.289\\
\textbf{Mathematics}& \input & \input & \input \\
\end{tabluar}
Now calculate the test statistic \chi^2=\input as the sum of all values in this table.
Input the test statistic to 3 decimal places.
c)
d)