Inequality in Wages in Europe

One question of interest to economists and other social scientists is the extent to which the strengthening of relationships between the nations of Europe through the ratification of the European Union has reduced social and economic differences between nations. One specific question is whether the creation of European-wide labor markets have "leveled" wages across countries - that is, eliminated disparities between countries in wages. Unification was designed to help reduce inequalities, but it is uncertain the degree to which inequities persist. For example, do workers in Germany earn the same wages as workers in Spain who do the same jobs?

To study this question, Giancarlo Rossi has gathered wage information 150 employees of various automobile manufacturing plants in Europe. He interviewed 30 workers at 5 different plants, with each plant in a different nation. This was painstaking work for Herr Rossi. He stood at the streetcar stops outside each plant, interviewing workers and recording their income, which was measured in thousand of euros.

The data he collected can be represented as such:

Plant Observations (in 1000s of Euros) Average Wage SD of Wage
1 10, 15, 17,... 18 9
2 20, 25, 23,... 23 9
3 18, 19, 14,,... 20 9
4 26, 19, 13,... 15 9
5 14, 18, 18... 19 9

With these data, he is ready to determine whether the averages of these five groups of autoworkers are the same. He starts by generating a null hypothesis that all five groups have the same mean. In formula terms, that hypothesis is expressed through the following notation:

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Question: What is the alternate hypothesis for this question?

Your job is to calculate the necessary statistics to evaluate these hypotheses, using the figures in the table presented above. The formulae you need are given below. Use these to calculate values that can be plugged into the following table.

Source Sum of Squares Degrees of Freedom Mean Squares
Between BSS dfB Between Mean Squares
Within WSS dfW Within Mean Squares
Total TSS = BSS + WSS

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What do you conclude about the presence of wage inequality in Europe, given these figures?