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Thread: sample word problem, how to continue?

  1. #1
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    sample word problem, how to continue?


    μ=82μ=82
    2
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    I have this following problem to solve:"A factory produces rods which are planned to have a length of 80 cm. We assume that the length of the rods variates normaly having the normal distribution. We pick a sample of 100 rods and measure the length of each. We have the results that the arithmetic mean of the sample is 82 cm and the variance of the sample is 0,025 cm^2. Test the hypothesis that the length of the rods produced in the factory have the desired value 80 cm. The alternative hypothesis is that the length differs 80 cm from the desired value."


    I have solved the value t:

    t=μμ0S2n=82800.025100
    whe

    But how should I continue? What do I have left? This problem is confusing me..
    Thank you for your help!

    whe
    μ=82μ=82, μ0=80μ0=80, n=100n=100 and S2=0.025
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  2. #2
    MHF Contributor
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    Re: sample word problem, how to continue?

    $t = \dfrac{\mu - \mu_0}{\sqrt{\frac{\sigma^2}{n}}}$

    $t = \dfrac{82-80}{\sqrt{\frac{0.025}{100}}} \approx 126.5$

    this is such an enormous number for a test statistic that it makes me think you copied the sample variance incorrectly.

    At any rate given this statistic the probability that the produced rods conform to a population mean of 80cm (i.e. $H_0$) is 0.
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