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.

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

Answer 1

a)

We need to construct the 99% confidence interval for the difference between population proportions p1​−p2​. We have been provided with the following information about the sample proportions:

Favorable Cases 1 (X1​) =	63
Sample Size 1 (N1​) =	500
Favorable Cases 2 (X2​) =	30
Sample Size 2 (N2​) =	400

The sample proportion 1 is computed as follows:

The sample proportion 2 is computed as follows:

The critical value for α=0.01 is . The corresponding confidence interval is computed as shown below:

(b)

Correct solution is :-

(c)

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

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