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Math Help - estimated standard error

  1. #1
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    estimated standard error

    SAMPLE 1 SAMPLE 2

    Sample size 56 Sample size 55
    mean 3.2 mean 2.8
    s. deviation 1.8 s deviation 1.5


    How do i find the Estimated Standard Error of the difference between the 2 sample mean numbers.

    i know that ESE is S / Square root of N

    But dont know how to progress
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  2. #2
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    SE_1 = \frac{s_1}{\sqrt{n_1}}

    SE_1 = \frac{1.8}{\sqrt{56}}=\cdots

    SE_2 = \frac{s_2}{\sqrt{n_2}}

    SE_2 = \frac{1.5}{\sqrt{55}}=\cdots

    Now check out this link Confidence Interval
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  3. #3
    MHF Contributor matheagle's Avatar
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    The st. error is the estimate of the st. deviation.
    NOW there are two cases here.
    If you assume that the population variances are equal, you pool the sample variances.

    The st. deviation of \bar X_1-\bar X_2 is the square root of the variance \sqrt{ {\sigma^2_1\over n_1} + {\sigma^2_2\over n_2} }.

    Since we usually do not know \sigma^2_1 or \sigma^2_2 we use the sample variances

    and that's what we call the st. error, \sqrt{ {s^2_1\over n_1} + {s^2_2\over n_2} }.

    BUT in may cases we assume that \sigma^2_1=\sigma^2_2 and in that case we pool the two estimators,

    here the st. error is s_p\sqrt{{1\over n_1} + {1\over n_2} } which is the same as \sqrt{ {s^2_p\over n_1} + {s^2_p\over n_2} }.
    Last edited by matheagle; June 10th 2009 at 04:20 PM.
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