Reducing scrap of 4-foot planks of hardwood is an important factor in reducing cost at a wood-flooring manufacturing company. Accordingly, engineers at Lumber works are investigating a potential new cutting method involving lateral sawing that may reduce the scrap rate. To examine its viability, samples of 500 and 400 planks, respectively, were examined under the old and new methods. Sixty-two of the 500 planks were scrapped under the old method, whereas 36 of the 400 planks were scrapped under the new method.
a. Construct the 95% confidence interval for the difference between the population scrap rates between the old and new methods, respectively.
b. Specify the null and alternative hypotheses to test for differences in the population scrap rates between the old and new cutting methods, respectively.
c. Using the results from part (a), can we conclude at the 5% significance level that the scrap rate of the new method is different than the old method?