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Finding the value for rejection region using some kind of table

  1. Dec 14, 2009 #1
    I'm lost no how to find the cutoff rejection region and which table to use?

    This is an example,

    n 34
    X-bar 10.3
    s 3.1

    98% Confidence Interval for µ is
    10.3 ± 2.33 x 0.5316
    = (9.0632 , 11.5368)

    H0: µ ≤ 9
    H1: µ > 9

    Tests Z-stat = 1.3 = 2.4452
    Statistic 0.5316

    Significance Level = 0.01

    Rejection Region =
    Tail = RIGHT
    Cutt -Off = Z-alpha = 2.326
    Decision = Reject H0

    p-value = 0.0072

    I understand how they reject H0, but I am lost how they got 2.326. I think it's in the Z-table but I'm not sure, can someone explain to me clearly. It would also help if you can tell me how to find 0.0072 for the p-value.
  2. jcsd
  3. Dec 15, 2009 #2


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    Homework Helper

    I'm not sure how your Z table is set up - whether it gives only tail areas or cumulative probabilities.

    If it gives tail areas (areas to the right of specific Z-values, do this: look through the AREAS for 0.01 - the associated Z-value will be 2.326

    If your Z- table gives cumulative probabilities (areas of the form P(Z <=z)), look for the area that is closest to 0.99 (this is 1 - 0.01) - again, the Z-value should be 2.236.

    Some tables only give the area between 0 and specified values of Z. If this is the case, look through the areas for the value closest to 0.49 - again, you should find Z = 2.236.
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