In intaglio printing, design or figure is carved beneath surface of hard metal or stone. Business objective of intaglio printing company is to find out whether there are differences in mean surface hardness of steel plates, based on two different surface conditions - untreated and treated by lightly polishing with emery paper. Experiment is created in which 40 steel plates are arbitarily assigned - 20 plates are untreated and 20 plates are treated. Results of experiment are as follows:

Hardness
Untreated Treated
164.4 177.1 158.2 150.2
159.0 163.9 138.2 155.6
153.9 167.8 168.0 151.2
165.1 160.8 149.7 158.7
157.2 167.4 145.5 151.2
154.5 163.5 168.2 150.9
160.9 164.5 154.3 161.7
164.9 171.2 162.8 157.0
169.1 175.0 161.0 156.7
175.3 166.3 167.7 147.9

Suppose that population variances from both conditions are equal is there evidence that treatment decreases  surface hardness of steel plates? Solve manually. Use alpha = 0.05) Point to your decision rule, hypotheses and statistical and management conclusions.