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Math Help - Serious interval estimation problem

  1. #1
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    Smile Serious interval estimation problem

    Q.
    The electro-motive force (emf) of batteries produced by a company is normally distributed with mean and variance of 45.1 and 0.0016 respectively .
    If 4 such batteries are connected in series ,find the 50% confidence interval of the mean emf .How do you explain the results to a non-statistician ??

    We are already given the mean and the variance of the population .
    So here what is meant by 50% confidence interval ?

    Can somebody help me to answer this question ?
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  2. #2
    MHF Contributor matheagle's Avatar
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    A 50 percent confidence interval is lame.
    That means that the coverage isn't very good.
    It says that in the long run (law of large numbers)
    half of your intervals will contain the mean and half won't.
    Not a desireable result at all.
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  3. #3
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    Thumbs down

    Quote Originally Posted by matheagle View Post
    A 50 percent confidence interval is lame.
    That means that the coverage isn't very good.
    It says that in the long run (law of large numbers)
    half of your intervals will contain the mean and half won't.
    Not a desireable result at all.
    I could not understand about what you are talking .
    Why are we searching for a 50% confidence interval here since we know the population parameter ?
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  4. #4
    MHF Contributor matheagle's Avatar
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    I thought you had sample estimates.
    IF you know the population parameters, why would you do any estimation?
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  5. #5
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    Smile

    Quote Originally Posted by matheagle View Post
    I thought you had sample estimates.
    IF you know the population parameters, why would you do any estimation?
    but that is the actual problem I got .
    is there any other meaning of that problem ?
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  6. #6
    MHF Contributor matheagle's Avatar
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    with mean and variance of 45.1 and 0.0016 respectively .


    Are you sure that these are not the sample estimates?
    I orginally thought that they were.
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  7. #7
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    sure you are correct ...
    they should be otherwise the question is meaningless isn`t it
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  8. #8
    MHF Contributor matheagle's Avatar
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    The only thing I can think of, but that involves repeated confidence interval estimation is an exercise I did out of wackerly's book.
    I made my students generate 100 uniforms on excel, then transform then to exponentials with a set mean. WE knew the mean.
    Then they obtained a 95 percent CI for that known mean.
    I made them do that 100 times, so there were 100 times 100= 10,000 observations.
    Approximately 95 percent of these intervals contained that mean.
    Some students had 93, others had 96 of them containing the mean.
    That's the only thing I can think of.
    They can see if the interval truly contains the mean.
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  9. #9
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    so with this question can we perform such a thing although we have 4 batteries .
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  10. #10
    MHF Contributor matheagle's Avatar
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    sure, but you need normality
    it would be a t density with 3 degrees of freedom, thats with s.
    and you should do it over and over again.
    HOWEVER if you know sigma, it's a normal rv.
    It's the (strong) law of large numbers.
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  11. #11
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    Smile please

    Quote Originally Posted by matheagle View Post
    The only thing I can think of, but that involves repeated confidence interval estimation is an exercise I did out of wackerly's book.
    I made my students generate 100 uniforms on excel, then transform then to exponentials with a set mean. WE knew the mean.
    Then they obtained a 95 percent CI for that known mean.
    I made them do that 100 times, so there were 100 times 100= 10,000 observations.
    Approximately 95 percent of these intervals contained that mean.
    Some students had 93, others had 96 of them containing the mean.
    That's the only thing I can think of.
    They can see if the interval truly contains the mean.
    Quote Originally Posted by matheagle View Post
    sure, but you need normality
    it would be a t density with 3 degrees of freedom, thats with s.
    and you should do it over and over again.
    HOWEVER if you know sigma, it's a normal rv.
    It's the (strong) law of large numbers.

    that is what I did first ,but the problem came after solving the question
    Can you please show me the steps of repeating the process ?
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