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24 August, 21:38

A sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.41 mpa and a sample standard deviation of 0.77 mpa.

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  1. 24 August, 21:43
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    For this problem, the confidence interval is the one we are looking for. Since the confidence level is not given, we assume that it is 95%.

    The formula for the confidence interval is: mean ± t (α/2) (n-1) * s √1 + 1/n

    Where:

    α = 5%

    α/2 = 2.5%

    t 0.025, 19 = 2.093 (check t table)

    n = 20

    df = n - 1 = 20 - 1 = 19

    So plugging in our values:

    8.41 ± 2.093 * 0.77 √ 1 + 1/20

    = 8.41 ± 2.093 * 0.77 (1.0247)

    = 8.41 ± 2.093 * 0.789019

    = 8.41 ± 1.65141676

    = 6.7586 < x < 10.0614
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