2. A university awards its graduates a degree in one of three categories, Distinction, Merit or Pass.
Table 1 shows information about a random sample of 200 graduates from three departments, Arts, Humanities and Sciences.
\begin{table}[h]
| \cline { 2 - 5 }
\multicolumn{1}{c|}{} | Arts | Humanities | Sciences | Total |
| Distinction | 22 | 32 | 38 | 92 |
| Merit | 15 | 30 | 13 | 58 |
| Pass | 18 | 15 | 17 | 50 |
| Total | 55 | 77 | 68 |
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{table}
Xiu wants to carry out a test of independence between the category of degree and the department.
Table 2 shows some of the values of \(\frac { ( O - E ) ^ { 2 } } { E }\) for this test.
\begin{table}[h]
| \cline { 2 - 5 }
\multicolumn{1}{c|}{} | Arts | Humanities | Sciences | Total |
| Distinction | 0.43 | 0.33 | 1.44 | 2.20 |
| Merit | 0.06 | 2.63 | 2.29 | 4.98 |
| Pass | | | | |
|
\captionsetup{labelformat=empty}
\caption{Table 2}
\end{table}
- Complete Table 2
- Hence, complete Xiu's hypothesis test using a \(5 \%\) level of significance. You should state the hypotheses, the degrees of freedom and the critical value used for this test.