Analysing Confidence Levels
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As part of the quality control process, samples of parts are periodically taken for measurement to see if they conform to specifications. In one sample the diameter of a part is measured with the following results:
x_m1 = 3.56 mm, σ_1 = 0.06 mm, n_1 = 20
A second sample is taken with the following results:
x_m2 = 3.58 mm, σ_2 = 0.03 mm, n_2 = 23
Examine these data to determine if they yield the same results with a confidence level of 90 percent. Repeat for a confidence level of 95 percent.
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Hypotheses: H0: (m1 - m2) = 0 vs. Ha: (m1 - m2) ¹ 0
Test Statistic: where
Level of significance: , 1 - 0.95 = 0.05
Rejection region: t < -ta/2 or t > ta/2, and the distribution of t is based on (n1 + n2 - 2) degrees ...
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