Productivity is the key driver of wages and one of the most important determinants of living standards. The British Chambers of Commerce commissioned research into understanding whether labour productivity in the automotive manufacturing sector in England and Ireland were the same or different. The researchers collected data on a random sample of 8 firms in England and 4 in Ireland and recorded productivity in units of value added () per hour. It is assumed that firm-level productivity has a normal distribution.

The following data were collected:

England 39 45 50 43 35 43 39 50

Ireland. 56 43 68 47

Set up appropriate null and alternative hypotheses and conduct a test of the hypotheses of equal mean productivity in England and Ireland at 5 per cent significance level under the assumption of unknown but equal population variances. Provide as much detail as possible on your procedures. Clearly show all your steps in testing and state your decision. Discuss the economic implications of your findings. Do you think the assumption of equal population variances is justified?