12.51 An experiment was conducted to determine the effects of two alloying elements (carbon and manganese) on the ductility of specimens of metal. Two specimens from each treatment were measured, and the data (in work required to break a specimen of standard dimension) are listed in table below.

a Perform an analysis of variance, conducting all appropriate tests at the 5% significance level.
b Which treatment would you recommend to maximize average breaking strength?
Why?

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Carbon 0.2% 0.5% 0.5% 34.5 38.2 37.5 39.4 Manganese 1.0% 36.4 42.8 37.1 43.4