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21 December, 00:19

Two kinds of thread are being compared for strength. fifty pieces of each type of thread are tested under similar conditions. brand a has an average tensile strength of 78.3 kilograms with a standard deviation of 5.6 kilograms, while brand b has an average tensile strength of 87.2 kilograms with a standard deviation of 6.3 kilograms. construct a 95% confidence interval for the difference of the population means.

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  1. 21 December, 00:40
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    Let x = 78.3

    y = 87.2

    σₓ = 5.6 and σ (y₎ = 6.3

    number of pieces n = 50

    z = z-score value = 1.96 in this case

    A 100 (1-α) % confidence interval for the difference in large sample means is:

    (x - y) ± z x √ (σₓ² / n + σ (y₎² / n)

    by putting the values,

    = (78.3-87.2) ± 1.96 x √ (5.6² / 50 + 6.3² / 50)

    = - 8.9 ± 2.34

    = [-11.24, - 6.56]
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