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Notes on Topic 8:
Hypothesis Testing

    Sampling Distribution of Means for Alcohol Effect on Birthweight Data


    To determine the sampling distribution of means for this empirical situation, we must

    • Determine the standard error of the mean (standard deviation of the distribution of sample means) for samples of size 16.
    We must also make assumptions about the distribution of birthweight in the population of rats. Presumably, past record keeping lets us reasonably assume that:
    • The population has a mean birthweight of 18 grams.
    • The population has a standard deviation of 4.
    Thus, the population distribution is:

  1. We recall that the standard error is calculated by the formula:

    Thus, for our empirical situation, the value is

    4/sqrt(16) = 1

    Thus, the sampling distribution is:

  2. 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: