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.