A business company needs to know how to compare worker production between two di
ID: 2956020 • Letter: A
Question
A business company needs to know how to compare worker production between two different departments, department X and department Y. Each department has 5 workers in it that are given a productivity score based on units produced. Department X has better machinery and therefore workers in this department produce units at a faster rate. Department X's workers have the following productivity scores: 330, 304, 295, 287, and 280. Department Y's workers have the following productivity score: 220, 214, 205, 200, and 186.Based on the information given, determine who is more productive: the worker with a score of 330 in department X or the worker with score 220 in department Y.
Explanation / Answer
Dep X: 330, 304, 295, 287, 280 nx = 5 Xmean = (330 + 304 + 295 + 287 + 280)/5 = 299.2 S^2(x) = (330^2 + 304^2 + 295^2 + 287^2 + 280^2 - 5*299.2^2)/4 = 376.7 ny = 5 Ymean = (220 + 214 + 205 + 200 + +186 )/5 = 205 S^2(y) = (220^2 + 214^2 + 205^2 + 2002 + 186^2 - 5*205^2 )/4 = 173 H0: mu(x) = m(y) H1: mu(x) ? m(y), alpha = 0.05 S^2(x - y) =sqrt(((5 - 1)·376.7 + (5 - 1)·177)/8)* sqrt(1/5 + 1/5) = 10.52330746 Decision Rule: If abs((Xmean - Ymean) - (mu(x) - mu(y))/10.52330746 > tst(8, 0.975) Reject H0. If 8.95 > 2.306, Reject H0. Conclusion: More productive is the worker with a score of 330 in department X
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