Question 4

In the city of Burgham, a random sample of 120 city workers were asked their opinion about the city council's "No Jab - No Job" proposal - which involves the council only employing workers who had been vaccinated. As part of marketing this proposal, the council wish to understand whether there was a relationship between the category of employee, and their opinion. The data is summarised in the table below.

	|	Blue Collar	|	White Collar	|	Executives	|	Managers	|	TOTAL
------------	+	------------	+	------------	+	------------	+	------------	+	------------
In favour	|	24	|	12	|	3	|	2	|	41
------------	+	------------	+	------------	+	------------	+	- ----------	+	------------
Against	|	11	|	16	|	2	|	4	|	33
------------	+	------------	+	- ----------	+	------------	+	------------	+	------------
Indifferent	|	19	|	14	|	5	|	8	|	46
------------	+	------------	+	------------	+	------------	+	------------	+	-------- ---
TOTAL	|	54	|	42	|	10	|	14	|	120

a) Being careful to state your conclusions, and using a level of significance of alpha = 10%, test whether workers' opinion of the proposal is independent of their employment category.

b) The council's Human Resource Manager claims that your conclusion from part [a] proves that being a blue collar will cause one to have a different opinion of the proposal to a white collar worker. Explain whether the Human Resource Manager is correct.