Finding the value for rejection region using some kind of table...

  1. I'm lost no how to find the cutoff rejection region and which table to use?

    This is an example,
    Data

    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)

    Hypothesis
    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. statdad

    statdad 1,455
    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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