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Math Help - sampling distributions and estimators

  1. #1
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    sampling distributions and estimators

    Suppose that each of 2 statisticians A and B independently takes a random sample of 20 observations from a normal distribution for which the mean mu is unknown and the known value of the variance is 4. suppose also that statistician A finds the sample variance in his random sample to be 3.8. and statistician B finds the sample variance in her random sample to be 9.4. For which random sample is the sample mean likely to be closer to the unknown value of mu??

    Any hints or explanations would be greatly appreciated. Do I need to compare z scores maybe?
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  2. #2
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    Quote Originally Posted by holly123 View Post
    Suppose that each of 2 statisticians A and B independently takes a random sample of 20 observations from a normal distribution for which the mean mu is unknown and the known value of the variance is 4. suppose also that statistician A finds the sample variance in his random sample to be 3.8. and statistician B finds the sample variance in her random sample to be 9.4. For which random sample is the sample mean likely to be closer to the unknown value of mu??

    Any hints or explanations would be greatly appreciated. Do I need to compare z scores maybe?
    Since the distribution of sample variances has no dependence on sample mean (or population mean) for this case the sample variances provide no information about the difference between population mean and sample means.

    A more rigorous argument for this can be made by a Bayesian analysis of the problem.

    CB
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