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)

Step 4: p-value range

Calculate ν, the degrees of freedom, for this test.
v=\input
Use tables to find a range for your p-value. Choose from the options below.
p is bigger than 10%
p lies between 10% and 5%
p lies between 5% and 1%
p is smaller than 1%
d)

Step 6: Conclusion

Given the p-value and the range you have found, what is the strength of evidence against the null hypothesis?
None Slight Moderate Strong
Your decision:
Retain H_0 Reject H_0
Your conclusion:
There is evidence to suggest an association between degree subject and performance.
There is no evidence to suggest an association between degree subject and performance.