Reducing scrap of 4-foot planks of hardwood is an important factor in reducing cost at a wood-flooring manufacturing company. Accordingly, engineers at Lumberworks 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-three of the 500 planks were scrapped under the old method, whereas 34 of the 400 planks were scrapped under the new method.(You may find it useful to reference the appropriate table:z tableort table)

a.Construct the 99% confidence interval for the difference between the population scrap rates between the old and new methods, respectively (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)