Comparing the populations
Although standard deviations in the two populations may also differ, we are usually most interested in the difference between the population means. Differences between the means can be expressed in terms of the model parameters with the following questions.
Randomness of sample difference
These questions are about µ2 - µ1 and the
best estimate of it is .
However,
cannot
give definitive answers since
it is random — it varies from sample to sample.
Without an understanding of the distribution of ,
it is impossible to properly interpret what the sample difference, 9.5 pieces,
tells you about the difference between the underlying population means.