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Thread: Deriving the form of the best size for exponential distribution

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    Deriving the form of the best size for exponential distribution




    Hi everyone

    So in this question I am told that a supermarket claims that the mean time to serve a customer is equal to 4 mins.However, a customer claims it is greater than 4 mins. I am asked based off a sample of n=9, determine the form of the best test of which has size of a=0.05

    So I know my Ho: λ=4 and my Ha: λ>4

    I am just unsure on how to derive it down, I know I use the central limit theorem like in previous examples I have done but very unsure for exponential distribution !

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    Re: Deriving the form of the best size for exponential distribution

    hi,
    what is exactly the question if you already have the sample size?

    regards

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    Re: Deriving the form of the best size for exponential distribution

    Clt might not be appropriate here. Have you worked with likelihood ratio tests before?
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    Re: Deriving the form of the best size for exponential distribution

    What will happen when 9 exponentially distributed variables are summed?

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    Re: Deriving the form of the best size for exponential distribution

    Quote Originally Posted by Dason View Post
    Clt might not be appropriate here. Have you worked with likelihood ratio tests before?
    Yep I have, this is what I believe I do but again unsure:

    Conduct the neyman-pearson lemma i.e. the likelihood ratios over one another. Then once I have these ratios I am basically solving down until I get something along the lines of
    P(sum of xi > ....) then from here I would use my CLT

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    Re: Deriving the form of the best size for exponential distribution

    Quote Originally Posted by GretaGarbo View Post
    What will happen when 9 exponentially distributed variables are summed?
    If these are summed it means that we would have a gamma distribution but I don't see how that would apply here

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    Re: Deriving the form of the best size for exponential distribution


    Quote Originally Posted by XeroPhobous View Post
    If these are summed it means that we would have a gamma distribution .....
    And what would it be under the null hypothesis?

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