Please without excel? Two processes are used to produce forgings used in aircraf

Question

Please without excel?

Two processes are used to produce forgings used in aircraft wing assembly. Of 260 forgings selected from process 1, 10 do not conform to the strength specifications, whereas of 380 forgings selected from process 2, 20 are nonconforming. a. Estimate the fraction nonconforming for each process b. Test the hypothesis that the two processes have identical fractions nonconforming against a two-sided alternative. Use alpha = 0.05. c. Construct a 95% confidence interval on the difference in fraction nonconforming between the two processes. What is your conclusion based on the confidence interval?

Explanation / Answer

Part a

For process 1, we are given

n = 260, x = 10

Fraction non-conforming = p1 = x/n = 10/260 = 0.038462

For process 2, we are given

n = 380, x = 20

Fraction non-conforming = p2 = x/n = 20/380 = 0.052632

Part b

Here, we have to use two sample z test for difference in two population proportions. The null and alternative hypotheses for this test are given as below:

H0: p1 = p2

Ha: p1 p2

This is a two tailed test.

We are given level of significance = alpha = 0.05

The test statistic formula is given as below:

Z = (p1 – p2) / sqrt[(p1q1/n1) + (p2q2/n2)]

Where, q1 = 1 – p1 and q2 = 1 – p2

Here, q1 = 1 - 0.038462 = 0.961538

And q2 = 1 - 0.052632 = 0.947368

Z = (0.038462 - 0.052632) / sqrt[(0.038462*0.961538/260) + (0.052632*0.947368/380)]

Z = -0.01417004/ 0.01653652

Z = -0.856893712

P-value = 0.3915

Alpha value = 0.05

P-value > Alpha value

So, we do not reject the null hypothesis that two processes have identical fractions non-confirming.

Part c

The confidence interval formula is given as below:

Confidence level = 95%

Critical Z value = 1.96

Confidence interval = (p1 – p2) -/+ Z*sqrt[(p1q1/n1) + (p2q2/n2)]

Confidence interval = (0.038462 - 0.052632) -/+ 1.96*sqrt[(0.038462*0.961538/260) + (0.052632*0.947368/380)]

Confidence interval = -0.01417004 -/+ 1.96*0.01653652

Confidence interval = -0.01417004 -/+ 0.0324

Lower limit = -0.01417004 - 0.0324 = -0.0466

Upper limit = -0.01417004 + 0.0324 = 0.0182

The value ‘0’ included in the interval, so we conclude that two processes have identical fractions non-confirming.

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