Question

A research assistant working for a large company wanted to investigate attitudes towards a proposed management buy-out. Thus she asked a random sample of the company’s workforce whether or not they were in favour of the buy out. The research assistant was particularly interested in finding out whether the workers’ views on the buy out were related to the classification of their job (manual or non-manual).

Altogether 120 workers were interviewed by her, of these 70 were manual workers and 50 were non-manual workers. Of the manual workers 30 were in favour of the buy out, whereas 25 of the non-manual workers were in favour.

1. Draw up a 2x2 table showing this information and carry out a test of association to see if job classification affects attitude to the proposed management buy-out.

Answer 1

The 2 x 2 table showing the given information here is given as:

	Manual Workers	Non Manual Workers	Total
Favour to buy	30	25	55
Not in favour to buy	40	25	65
Total	70	50	120

The expected values for each of the 4 clls is computed here as:
E_i = (Sum of row i)*(Sum of column i) / Grand Total

	Manual Workers	Non Manual Workers
Favour to Buy	55*70/120 = 32.08	55*50/120 = 22.92
Not in favour to buy	65*70/120 = 37.92	65*50/120 = 27.08

Using the above expected and the observed frequencies, the chi square test statistic here is computed as:

Degrees of freedom here is obtained as:
Df = (num of col - 1) (Num of rows - 1) = 1

Therefore the p-value here is obtained from the chi square distribution tables as:

As the p-value here is very high, we have sufficient evidence here that there is no association between the two variables.