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    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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