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-one of the 500 planks were scrapped under the old method, whereas 31 of the 400 planks were scrapped under the new method.

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. Round your answers to 2 decimal places.)

  Confidence interval is  % to  %.

b.

Select the null and alternative hypotheses to test for differences in the population scrap rates between the old and new cutting methods, respectively.

	H0: p1 − p2 = 0; HA: p1 − p2 ≠ 0
	H0: p1 − p2 ≤ 0; HA: p1 − p2 > 0
	H0: p1 − p2 ≥ 0; HA: p1 − p2 < 0

c.	Using the part a results, can we conclude at the 1% significance level that the scrap rate of the new method is different than the old method?

We (Click to select)(reject do not reject) H0. At the 1% significance level, we (Click to select)(can cannot) conclude the proportions are different between the old and new methods.

Answer 1

Ans:

a)

sample proportion for old method=61/500=0.122

sample proportion for new method=31/400=0.0775

point estimate=0.122-0.0775=0.0445

Margin of error=2.576*SQRT((0.122*(1-0.122)/500)+(0.0775*(1-0.0775)/400))=0.0511

lower limit=0.0445-0.0511=-0.0066

upper limit=0.0445+0.0511=0.0956

Confidence interval is  (-0.66% to 9.56%)

b)

H₀: p₁ − p₂ = 0;

H_A: p₁ − p₂ ≠ 0

c)As,confidence interval include 0 within its limits,we fail to reject null hypothesis.

We do not reject H₀. At the 1% significance level, we cannot conclude the proportions are different between the old and new methods.