Hypothesis testing and the power of the test

  1. I am having trouble understanding the concept of the power of the test. Here is a sample question with solution:

    A company wants to test if average weekly demand is more than 2000 lbs. Test is to be carried out at 5% level of significance, and an estimate of the population variance is 1,000,000. What is the power of the test if the true mean is 2300 lbs.

    So here is the sol'n (u represents population mean, and x represents x bar, sample mean, z is z-score, based on 5% is 1.645):

    Hypothesis statement: Null: u <= 2000 Alternative: u > 2000

    xcritical = u + zo (o is standard deviation, calculation shows it to be 200)
    xcritical = 2000 + 1.645(200)
    xcritical = 2349

    Power at 2300

    P(xcritical > 2349) = P (z > 0.145)
    P(z > 0.145) = 0.5 - 0.0596 = 0.4404

    So the thing i dont understand, is that if the power of the test is the probability of correctly rejecting the null hypothesis when it is false, why do we calculate the area beyond the z-score and call that the power of the test. Isnt the area beyond supposed to be Beta, the probability of making a type II error?

    Any help is greatly appreciated
  2. jcsd
  3. EnumaElish

    EnumaElish 2,332
    Science Advisor
    Homework Helper

    This is the probability that a statistical test will detect a defined pattern in data and declare the extent of the pattern as showing STATISTICAL SIGNIFICANCE. POWER is related to TYPE-2 ERROR by the simple formula : POWER = (1-BETA) ; the motive for this re-definition is so that an increase in value for POWER shall represent improvement of performance of a STATISTICAL TEST. For more detail, see : BETA.
    Also known as TYPE-2 ERROR, BETA is the complement to POWER : BETA = (1-POWER). This is the probability that a statistical test will generate a false-negative error : failing to assert a defined pattern of deviation from a null pattern in circumstances where the defined pattern exists.
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