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:
 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:
 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:
