A company that does manufacturing work has one facility that is automated and on

Question

A company that does manufacturing work has one facility that is automated and one that has manual functions. In order to estimate the difference in mean time it takes to complete a part on the two lines, the company has requested that a random sample of 16 parts at each facility be tracked from start to finish and the time required be recorded. The sample data to the right were recorded. Assuming that the populations are normally distributed with equal population variances, construct and interpret an 80% confidence interval estimate. Automated x1 53.6 hours s1 = 6.8 hours Manual x2 = 70.9 hours s: 7.9 hours The 80% confidence interval for the difference between the two population means or the length of time it takes to make a part rom start to sh is (Round to two decimal places as needed.)

Explanation / Answer

Standard error, SEx1-x2 = sqrt [ s21 / n1 + s22 / n2 ] = 2.605883

Degree of Freedom, DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] } = 29.3 = 29

tcrit = +/- 1.3114

80% CI = (53.6 - 70.9) +/- 1.3114*2.605883 = (-20.72, -13.88)

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