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Math Help - hypothesis testing

  1. #1
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    hypothesis testing

    (a) a sample of 14 children from parents without diabetes had a mean fasting glucose level of 82.2mg/dL with sample standard deviation 2.49mg/dL.
    give a 95% confidence interval for the underlying standard deviation of fasting glucose level for children from parents without diabetes.
    (b)a second sample of 14 children from parents both with type II diabetes had a mean fasting glucose level of 86.1mg/dL with sample standard deviation 2.09mg/dL. perform a hypothesis test to determine if the variability in glucose levels is the same for both groups of children. include a statement of H_{0} and H_{1}, the test statistic and its distribution under H_{0}
    (c) based on your answer to (b), perform a hypothesis test to determine if the mean glucose level is higher for children from parents with type II diabetes than from parents without diabetes. include a statement of H_{0} and H_{1}, the test statistic and its distribution under H_{0}
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by wik_chick88 View Post
    (a) a sample of 14 children from parents without diabetes had a mean fasting glucose level of 82.2mg/dL with sample standard deviation 2.49mg/dL.
    give a 95% confidence interval for the underlying standard deviation of fasting glucose level for children from parents without diabetes.
    (b)a second sample of 14 children from parents both with type II diabetes had a mean fasting glucose level of 86.1mg/dL with sample standard deviation 2.09mg/dL. perform a hypothesis test to determine if the variability in glucose levels is the same for both groups of children. include a statement of H_{0} and H_{1}, the test statistic and its distribution under H_{0}
    (c) based on your answer to (b), perform a hypothesis test to determine if the mean glucose level is higher for children from parents with type II diabetes than from parents without diabetes. include a statement of H_{0} and H_{1}, the test statistic and its distribution under H_{0}

    What have you tried? What is the specific difficulty you are having here?

    CB
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  3. #3
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    for part (a) i think i have figured it out...
    \sigma = ?
    n = 14
    s = 2.49

    from the chi-square-distribution table i got
    \chi^{2}_{13;0.025} = 5.01
    \chi^{2}_{13;0.975} = 24.7

    so a 95% confidence interval for \chi^{2} is
    (\frac{2.49^{2} * 13}{24.7},\frac{2.49^{2} * 13}{5.01})
    = (3.263, 16.088)

    so a 95% confidence interval for \chi is
    (1.806, 4.011)

    firstly, have i done this correctly? i was referring to the poorly set out example in our textbook! also, can u please explain why you use the values \gamma = 0.025 and 0.975 when referring to the chi-square-distribution table?
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  4. #4
    MHF Contributor matheagle's Avatar
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    You want .95 probability between any two percentiles
    so you can use those two, the .025 and the.975 percentiles, which most do
    That puts equal probability in each tail
    Or you can use one sided CIs where all the .05 is in one tail
    or use .02 and .97 etc.........

    And these are CIs for \sigma^2 and \sigma

    \chi^2 is the underlying distribution
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  5. #5
    MHF Contributor matheagle's Avatar
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    In part (b) you want to perfrom an F test comparing the two POPULATION variances
    Then in (c) you will a t test comparing the two means.
    NOW if you come away from (b) saying that the two st deviations are equal you
    will perform a pooled t test, where you pool the sample st deviations
    IF not you will use the non pooled test where you need to approximate the nasty degrees of freedom using satterwhite's approximation
    Student's t-test - Wikipedia, the free encyclopedia
    also http://www.bsos.umd.edu/socy/alan/ha..._two_means.pdf
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