SOLUTION: A production line is designed on the assumption that the difference between mean assembly times for two operations is five minutes. Independent tests for the two assembly operation

Question 824539: A production line is designed on the assumption that the difference between mean assembly times for two operations is five minutes. Independent tests for the two assembly operations yielded the following results.
Operation A: n1 = 25, xbar1 = 19.2, s1 = .73.
Operation B: n2 = 25, xbar2 = 13.68, s2 = .53.
At the 2% significant level, test the hypothesis that the difference between the mean assembly times is u1 - u2 = 5 minutes.
The p-value of the test statistic is:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A production line is designed on the assumption that the difference between mean assembly times for two operations is five minutes. Independent tests for the two assembly operations yielded the following results.
Operation A: n1 = 25, xbar1 = 19.2, s1 = .73.
Operation B: n2 = 25, xbar2 = 13.68, s2 = .53.
At the 2% significant level, test the hypothesis that the difference between the mean assembly times is u1 - u2 = 5 minutes.
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Ho: u1-u2 = 5
Ha: u1-u2 # 5
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Sample stat:: xbar1-xbar2 = 19.2-13.68 = 5.52
test statistic:: z(5.52) = (5.52-5)/sqrt[0.73^2/25 + 0.53^2/25] = 2.8821
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p-value = 2*P(z > 2.8821) = 2*normalcdf(2.8821,100) = 0.0039
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Conclusion: Since the p-value is less than 2%, reject Ho.
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Cheers,
Stan H.
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