A physical anthropologist has taken samples of skeletons at sites of two different prehistoric North American tribes. She wants to determine whether there is a difference between the skeletal heights of females in the tribes, because this will give valuable indirect information about dietary habits of the two cultures. The samples represent all of the skeletons she could find at the two sites that she could reliably identify as female and from which it was possible to estimate the height fairly accurately. Here is how the data came out:
tribe n mean SD ================================== 1 25 59.4 in 1.8 in 2 27 61.3 in 2.4 in
Set up a model for these data under the assumption (for the moment) that these are simple random samples from the populations of interest, and use the model to find a 95% confidence interval for the difference in average height among females in the two tribal populations and a significance test of the hypothesis that this difference is zero.