Difference in defect rates between two lines

Question

Production line 1 has 30 defects in 500 units; line 2 has 20 defects in 500. Construct a 95% confidence interval for the difference in defect rates (line 1 minus line 2), and state your conclusion.

Accepted Answer

Setup. Use (\hat{p}1 - \hat{p}2) \pm z^{}\sqrt{\hat{p}1(1-\hat{p}1)/n1 + \hat{p}2(1-\hat{p}2)/n2} with z^{} = 1.96. Here \hat{p}1 = 0.06, \hat{p}2 = 0.04, difference = 0.02. Compute the standard error. \sqrt{\frac{0.06 	imes 0.94}{500} + \frac{0.04 	imes 0.96}{500}} = \sqrt{0.0001128 + 0.0000768} = \sqrt{0.0001896} = 0.0138. Margin of error = 1.96 	imes 0.0138 = 0.027, so 0.02 \pm 0.027 = [-0.007,\ 0.047]. Interpret. The interval includes zero, so the apparent 2-point gap in defect rates is not statistically significant at the 5% level. Line 1 may simply have had a run of bad luck. Takeawa…

Difference in defect rates between two lines

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