Question

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 30 of the 400 planks were scrapped under the new method. Construct the 99% confidence interval for the difference between the population scrap rates between the old and new methods, respectively

Answer 1

	old method	New Method
x=	63	30
n =	500	400
p̂=x/n=	0.1260	0.0750
estimated diff. in proportion=p̂1-p̂2=		0.0510

Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) =

0.0198

for 99 % CI value of z=		2.576	from excel:normsinv((1+0.99)/2)
margin of error E=z*std error =		0.051108
lower bound=(p̂1-p̂2)-E=		-0.0001
Upper bound=(p̂1-p̂2)+E=		0.1021
from above 99% confidence interval for difference in population proportion =(-0.0001, 0.1021)