The diameter of holes for a cable harness is known to have a normal distribution with σ = 0.01 inches. A random sample of size 10 yields an

Question

The diameter of holes for a cable harness is known to have a normal distribution with σ = 0.01 inches. A random sample of size 10 yields an average diameter of 1.5045 inches. Find a 99% two-sided confidence interval on the mean hole diameter. Round the answers to 4 decimal places.

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Piper 2 weeks 2021-10-13T23:21:09+00:00 1 Answer 0

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    2021-10-13T23:22:40+00:00

    Answer: (1.4964, 1.5126)

    Step-by-step explanation:

    We know that the confidence interval for population mean is given by :-

    \overline{x}\ \pm z*\dfrac{\sigma}{\sqrt{n}}

    , where {\sigma= population standard deviation.

    n= sample size

    \overline{x} = Sample mean

    As per given , we have

    σ = 0.01 inches

    n= 10

    \overline{x}=1.5045

    Also, the critical value for 99% confidence interval = z*=2.576 [From x-value table.]

    [Significance level =1-0.99=0.01 and z_{\alpha/2}\ at\ \alpha=0.01 is 2.576.]

    Then, the 99% two-sided confidence interval on the mean hole diameter will be :-

    1.5045\ \pm (2.576)\dfrac{0.01}{\sqrt{10}}\\\\\approx1.5045\pm(2.576)(0.00316)=1.5045\pm0.00814016=(1.5045-0.00814016,\ 1.5045+0.00814016)\\\\=(1.49635984,\ 1.51264016)\approx(1.4964,\ 1.5126)

    Hence, the required confidence interval = (1.4964, 1.5126)

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