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    Biostatistics Problem to Reject or Accept Hypothesis

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    I have attached a long regression problem that I completed most of. I'd like you to tell me what I did wrong including incorrect calculations. Comments and hints would be also be greatly appreciated as I am just learning this. I know this is a long problem so Im offering 12 credits. Thanks.

    I have attached the problem as it was given to me (without my work) first. Then I attached my completed copy.
    -----------
    Assignment A, Module 3
    Please fill in all of the blank spaces below. Due May 17, 2004. (15 points)
    Obs# X Y X2 Y2 XY YCALC = a + bX YOBS - YCALC
    1 22 120
    2 20 115
    3 23 100
    4 21 100
    5 20 110
    6 24 145
    7 24 140
    8 27 180
    9 23 125
    10 28 210
    11 23 120
    12 26 160
    13 25 150
    14 29 225
    15 30 200
    16 28 175
    17 27 180
    18 23 130

    :
    Mean
    n = number of X-Y pairs = (X)2 = (Y)2 =
    df = (number of paired observations) - 2 = n - 2 =
    b = {(XY) - [(X)(Y)/n]} =
    (X2) - (X)2/n
    or
    b = {[n((XY))] - [(X)(Y)]}/{[n((X2))] - [(X)2]}
    =

    or
    b = SSXY/SSX = ([(XY)] - [(X)(Y)/n])/([ (X2)] - [(X)2/n]) =

    SSXY = [(XY)] - [(X)(Y)/n] =
    SSX = [(X2)] - [(X)2/n] =

    a = YMEAN - b(XMEAN) =

    YCALC =

    Module 3 Assignment A (Page 2)

    Obs#
    X
    Y xi =
    Xi - meanX
    xi2 yi =
    Yi - meanY
    yi2
    xiyi
    1 22 120
    2 20 115
    3 23 100
    4 21 100
    5 20 110
    6 24 145
    7 24 140
    8 27 180
    9 23 125
    10 28 210
    11 23 120
    12 26 160
    13 25 150
    14 29 225
    15 30 200
    16 28 175
    17 27 180
    18 23 130

    :
    Mean
    s2
    s

    (sx)2 = [(Xi - meanX)2]/(n - 1) = [(xi2)]/(n - 1) =
    (sy)2 = [(Yi - meanY)2]/(n - 1) = [(yi2)]/(n - 1) =
    (sy·x)2 = (n - 1)[(sy)2 - (b2)(sx)2]/(n - 2) =

    (sa)2 = [(sy·x)2/n] + {[(sy·x)2(meanX)2]/[(n - 1)(sx)2]}
    =

    sa =

    (sb)2 = (sy·x)2/[(n - 1)(sx)2] =

    sb =

    Module 3 Assignment A (page 3):

    Ho: b = 0.0000 : 0.05

    tCALC = b/sb = df = n - 2 =

    tTABLE(0.05) = therefore reject or fail to reject Ho that b = 0.0000 (choose one)

    95% CI for b: b ± (tTABLE)(sb) =

    therefore, 95% CI for b:
    therefore, reject or fail to reject Ho that b = 0.000 (choose one)

    ...............
    Ho: b = 1.0000 : 0.05

    tCALC = (b - 1.0000)/sb =

    tTABLE = therefore reject or fail to reject Ho that b = 1.0000 (choose one)

    95% CI for b: b ± (tTABLE)(sb) =

    therefore, 95% CI for b:
    therefore, reject or fail to reject Ho that b = 1.0000 (choose one)

    ..............
    Ho: b = 0.0000 : 0.05

    FCALC = MS(R)/MS(E) = SS(R)/MS(E) = (b2)(SSX)/MS(E)
    =

    MS(E) = SS(E)/(n - 2) =
    (or, MS(E) = [(sb)2](SSX) =
    SS(E) = SS(TOTAL) - SS(R) =
    SS(R) = (b2)(SSX) =
    SS(TOTAL) = SSY = [(Y2)] - [(Y)2/n] =

    FTable; 0.05; 1, (n - 2) = therefore reject or fail to reject Ho that b = 0.0000 (choose one)

    Module 3 Assignment A (page 4):

    95% Confidence Interval for regression line (at a given value of X):

    95% CI: yCALC ± [(ttable)(syCALC)]

    (syCALC)2 = [(sy·x)2/n] + {[(sy·x)2(X - meanX)2]/[(n - 1)(sx)2]}

    if X = 28.6111:

    (syCALC)2 =

    (syCALC) =

    YCALC =

    yCALC ± [(ttable)(syCALC)] =

    95% CI:

    Module 3 Assignment A (page 5):

    95% Confidence Interval for an individual calculated value of Y:

    If, once the regression line has been calculated from a set of X-Y observations, it is desired to calculate Y for an individual whose value of X is 28.6111, the 95% CI for that individual's calculated value of Y is: yCALC ± [(ttable)(syNEW)]

    (syNEW)2 = (sy·x)2 + [(sy·x)2/n] + {[(sy·x)2(X - meanX)2]/[(n - 1)(sx)2]}
    =

    (syNEW) =

    YCALC =

    yCALC ± [(ttable)(syNEW)] =

    95% CI:

    Module 3 Assignment A (page 6):

    r = {(XY) - [(X)(Y)/n]} =
    {[(X2) - (X)2/n] [(Y2) - (Y)2/n]}1/2

    or
    r = [(X - meanX)(Y - meanY)]/{[ (X - meanX)2][ (Y - meanY)2]}1/2
    = [(xiyi)]/{[(xi2)][(yi2)]}1/2 =

    or
    r = (b)(sx)/(sy) =
    or
    r = SSXY/{(SSX)(SSY)}1/2 =

    Ho: r = 0.0000 : 0.05

    tCALC = r/sr =

    sr = {(1 - r2)/(n - 2)}1/2 =

    tTABLE(0.05) = therefore reject or fail to reject Ho that r = 0.000 (choose one)

    ...............
    using table values for r:

    Ho: r = 0.0000 : 0.05 rTABLE(0.05) =

    therefore reject or fail to reject Ho that r = 0.0000 (choose one)

    ................
    Using F-ratio for regression:

    FCALC = MS(R)/MS(E) = SS(R)/MS(E) = (b2)(SSX)/MS(E)
    =
    FTable(0.05) =
    therefore reject or fail to Ho that r = 0.0000 (choose one)

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    https://brainmass.com/statistics/correlation-and-regression-analysis/biostatistics-problem-reject-accept-hypothesis-19401

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    Solution Summary

    The expert examines biostatistic problems to reject or accept hypothesis tests. The F-ratio for regression is used.

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