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Math Help - Use T-Statistic? Or use the Z value?

  1. #1
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    Exclamation Use T-Statistic? Or use the Z value?

    1. The local Tupperware dealers earned these commissions last month:

    $4377.47 $3183.76 $1970.16 $2270.88 $3860.06
    $2508.55 $1569.64 $4205.30 $1663.68 $3960.71

    Assuming the population for the amount of commissions earned by Tupperware dealers last month is known to be normally distributed, create a 95% confidence interval estimate for , the mean amount of commission earned.

    You will be asked to identify x-bar, s, alpha, df, t, E and the confidence interval.

    My main Q here would be whether I would use Z statistic or I should use the T-statistic? also any idea on how to compute df?

    Cheers

    Darren
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  2. #2
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    Quote Originally Posted by darren_a1 View Post
    1. The local Tupperware dealers earned these commissions last month:

    $4377.47 $3183.76 $1970.16 $2270.88 $3860.06
    $2508.55 $1569.64 $4205.30 $1663.68 $3960.71

    Assuming the population for the amount of commissions earned by Tupperware dealers last month is known to be normally distributed, create a 95% confidence interval estimate for , the mean amount of commission earned.

    You will be asked to identify x-bar, s, alpha, df, t, E and the confidence interval.

    My main Q here would be whether I would use Z statistic or I should use the T-statistic? also any idea on how to compute df?

    Cheers

    Darren
    First question to ask: Do you know the population standard deviation? No?

    Second questions to ask: Is the value of n 50 or more (some folk are less conservative and use 30 or so)? No?

    Then you use the t-statistic with df = n-1 where n is the sample size. You should know these things!
    Last edited by mr fantastic; April 4th 2008 at 08:58 PM. Reason: Added the bit about less conservative folk.
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  3. #3
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    Darren,
    The T-Test is robust under non-Normal distributions. Even when you do not know that distribution. In the case you describe, T-Test should be used because you have just a sample and the population is Normally distributed... but the test can be applied only if you have more than 30 observations (many authors use more than 35... ). Whatever, you have 10.
    If this is a textbook example (and we can ommit the detail that I explained above), I would use T-Test because you do not know the population variance and the population is Normally distributed.
    Hope this helps.


    Federico.
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  4. #4
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    Quote Originally Posted by darren_a1 View Post
    1. The local Tupperware dealers earned these commissions last month:

    $4377.47 $3183.76 $1970.16 $2270.88 $3860.06
    $2508.55 $1569.64 $4205.30 $1663.68 $3960.71

    Assuming the population for the amount of commissions earned by Tupperware dealers last month is known to be normally distributed, create a 95% confidence interval estimate for , the mean amount of commission earned.

    You will be asked to identify x-bar, s, alpha, df, t, E and the confidence interval.

    My main Q here would be whether I would use Z statistic or I should use the T-statistic? also any idea on how to compute df?

    Cheers

    Darren

    Darren,

    From you sample population, I calculate \overline{x} =  2957.021 and \sigma =  1034.0950. I got that from here: Mean, Variance, and Standard Deviation

    You had asked about how to calculate the t-statistic. I built this for you tonight. For the answer to your problem, I get:  2217.2600 < \mu < 3696.7820

    Go here: Student t-Test Confidence Interval for Mean

    We know n = 10, and you want a 95% confidence interval for the mean. Enter those values and take a look at the answer and the math work involved. This will show you how to do this in the future. I built a note in the math for how to calculate the t-score value based on \alpha using Excel's TINV function.

    For future reference, this lesson is located on the statistics menu and is searchable by confidence, interval, student-t, mean.

    Let me know if you have questions.
    Last edited by mathceleb; April 4th 2009 at 09:08 AM.
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  5. #5
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    Quote Originally Posted by falcald View Post
    Darren,
    ... but the test can be applied only if you have more than 30 observations (many authors use more than 35... ).
    Student's t-test is a small sample test for normally distributed data with unknown variance. If we has a known variance then a z-test would be appropriate, similarly if we have a large sample size.

    If we had a sample size were 30 or more we would be tempted to use a z-test (though I would hold out for a sample size of 100 myself).

    RonL
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