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Math Help - hypothesis testing, poisson distribution

  1. #1
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    hypothesis testing, poisson distribution

    At one stage of a water treatment process the number of particles of foreign matter per litre present in the water has a poisson distribution with mean 10. The water then enters a filtration bed which should extract 75% of foreign matter. The manager of the treatment works orders a study into the effectiveness of this filtration bed. 20 samples, each of 1 litre, are taken from the water and 64 particles of foreign matter are found. Using a suitable approximation test, at the 5% level of significance, weather or not there is evidence that the filter bed is failing to work properly.
    I know what approximation to use, ( the normal distribution) however I can't seem to work what value the of  \lambda is in 20 samples.

    Any help appreciated,
    Thank you.
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  2. #2
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    Unimaginative Reply Title

    H0: The filtration system is operating correctly
    H1: The filtration system is not operating correctly

    Therefore under H0, which we will assume for our model,
    the matter present in a litre of water should be Poisson distributed with lambda = 2.5

    Since we can add the means of collected Poisson distributions,
    for the twenty litres collectively, we should have a Poisson distribution with lambda = 2.5 + 2.5 + 2.5 ...
    = 20*2.5
    = 50
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  3. #3
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    Quote Originally Posted by mdruett View Post
    H0: The filtration system is operating correctly
    H1: The filtration system is not operating correctly

    Therefore under H0, which we will assume for our model,
    the matter present in a litre of water should be Poisson distributed with lambda = 2.5


    Since we can add the means of collected Poisson distributions,
    for the twenty litres collectively, we should have a Poisson distribution with lambda = 2.5 + 2.5 + 2.5 ...
    = 20*2.5
    = 50
    thank you, but I don't understand where you got 2.5 from? If the null hypothesis is true, than there is a mean of 10 foreign particles per litre, and we have 20 samples, so I thought you multiply.

    can you please explain further? how did you get 2.5?

    thank you
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  4. #4
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    Still short of a decent title

    H0: is that the filtration system is working properly.

    There are a mean of 10 particles per litre before it enters the filtration system.

    The filtration system removes 75% of this, under H0

    Therefore after the filtration system (where you'd have to take the samples from if you were going to check whether it was working)
    there are only 25% of the particles left under H0

    ie the mean should be = 0.25 * 10
    This is lamdba
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  5. #5
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    Quote Originally Posted by mdruett View Post
    H0: is that the filtration system is working properly.

    There are a mean of 10 particles per litre before it enters the filtration system.

    The filtration system removes 75% of this, under H0

    Therefore after the filtration system (where you'd have to take the samples from if you were going to check whether it was working)
    there are only 25% of the particles left under H0

    ie the mean should be = 0.25 * 10
    This is lamdba
    I understand now, was not thinking of the 75% taken out,

    thanks!
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