Last week, students measured their right and left hand spans and then calculated the difference (dominant hand span - opposite hand span). The research question is, "Is hand span greater, on average, for the dominant hand than for the non-dominant hand?" The relevant parameter in this scenario is the population mean difference (_diff).

For a STAT 100 class of forty (n=40) students, the differences in hand span had an average of 3.39mm with a standard deviation of 7.58mm.

1. What is the standard error of the mean in this situation? Show your computations.

2. Find the test statistic (z-score) and then the p-value. Show your computations for the z-score and explain how you found the p-value.

What do you conclude? Why?

3. If we had analyzed the data for multiple STAT 100 classes (i.e., more than 40 students) instead of only one, then

4. If we had data for only 20 students instead of 40, then