An experiment was conducted to determine whether surface finish has an effect on the endurance limit of steel. An existing theory says that polishing increases the average endurance limit (reverse bending). From a practical point of view, polishing should not have any effect on the standard deviation of the endurance limit, which is known from the performance of numerous endurance limit experiments to be 4000 psi. An experiment was performed on 0.4% carbon steel using both unpolished and polished smooth-turned specimens. The data are as follows: Find a 95% confidence interval for the difference between the population means for the two methods, assuming that the populations are approximately normally distributed.

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Endurance Limit (psi) for: Unpolished 0.4% Carbon Polished 0.4% Carbon 85,500 82.600 82,400 91.900 89,400 84.000 89.900 81,700 79,500 79.400 69,800 79.900 83.400 78.700 87,500 83,100