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Notes on Topic 8:
Hypothesis Testing

    Non-Directional (two-tailed) Techniques

    We can answer the question (i.e., we can test the hypothesis)

    "How likely are we to get this sample if the null hypothesis is true?"
    by testesting the null hypothesis stated below:

    There are four steps involved in hypothesis testing:

    1. State the Hypotheses:
      • Null hypothesis: No effect for alcohol consumption on birth weight. Their weight will be 18 grams. In symbols:
      • Alternative Hypothesis: ALcohol will effect birth weight. The weight will not be 18 grams. In symbols:
    2. Define the decision method:
      • (Classic Approach: Define Decision Criterion)

      • Determine the standard error of the mean (standard deviation of the distribution of sample means) for samples of size 16. The standard error is calculated by the formula:

        The value is 4/sqrt(16) = 1.

      • To determine how unusual the mean of the sample we will get is, we will use the Z formula to calculate Z for our sample mean under the assumption that the null hypothesis is true. The Z formula is:

        Note that the population mean is 18 under the null hypothesis, and the standard error is 1, as we just calculated. All we need to calculate Z is a sample mean.

        When we get the data we calculate Z and then look it up in the Z table to see how unusual the obtained sample's mean is, if the null hypothesis Ho is true, using a two-tailed probability.

    3. Gather Data:
      The two experimenters got these different sets of data:

      Experiment 1 Experiment 2
      Sample Mean = 13 Sample Mean = 16.5

    4. Evaluate Null Hypothesis:
      We calculate Z for each experiment, and then look up the P value for the obtained Z, and make a decision. Here's what happens for each experiment:
      Experiment 1 Experiment 2
      Sample Mean = 13
      Z = (13-18)/1 = -5.0
      p < .0000
      Reject Ho
      ViSta Applet
      Sample Mean = 16.5
      Z = (16.5-18)/1 = -1.5
      p = .1339
      Do Not Reject Ho
      ViSta Applet

      ViSta's Report for Univariate Analysis of Experiment 1 Data.

      ViSta's Report for Univariate Analysis of Experiment 2 Data.