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. A company is considering installing new machines to assemble its products. The company is considering two types of machines, but it will buy only one type. The company selected eight assembly workers and asked them to use these two types of machines to assemble products. The following table gives the time taken (in minutes) to assemble one unit of the product on each type of machine for each of these eight workers.

Machine I 23 26 19 24 26 22 20 18
Machine II 21 24 23 25 24 25 24 23

Test at the 5% significance level if the mean time taken to assemble a unit of the product is different for the two types of machines.

  • statistics -

    Calculate the mean and standard deviation for each machine.

    Z = (mean1 - mean2)/standard error (SE) of difference between means

    SEdiff = √(SEmean1^2 + SEmean2^2)

    SEm = SD/√(n-1)

    Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to that Z score.

  • statistic -

    Hypothesis Test: Independent Groups (z-test)

    Machine I Machine II
    22.25 23.63 mean
    3.06 1.30 std. dev.
    8 8 n

    -1.375 difference (Machine I - Machine II)
    1.175 standard error of difference
    0 hypothesized difference

    -1.17 z
    .2421 p-value (two-tailed)

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