Problem

A university awards degrees of Distinction, Merit and Pass.

A sample of 200 graduates is classified by faculty and degree classification. The results are shown in Table 1.

Degree classification	Arts	Humanities	Sciences	Total
Distinction	22	32	38	92
Merit	15	30	13	58
Pass	18	15	17	50
Total	55	77	68	200

Table 2 shows values of $\dfrac{(O-E)^2}{E}$ for some of the cells.

Degree classification	Arts	Humanities	Sciences	Total
Distinction	0.43	0.33	1.44	2.20
Merit	0.06	2.63	2.29	4.98
Pass

(a) Complete Table 2.

(b) Test, at the 5% level of significance, whether degree classification and faculty are independent. You should state your hypotheses, degrees of freedom and critical value.