A farmer wants to study the effect of letting her Holstein cows, Bos Taurus, roam freely compared to keeping them in a small pen. Specifically, she wants to know if they are less able to put on weight if they are restricted to a smaller space. She has a sample of 40 young cows of the same size to study. For each of the following scenarios, name the appropriate statistical test she should run and write the appropriate null hypothesis for each (you do not need to include the alternative hypotheses):?

a. She randomly divides her sample into two even groups and raises one group in the pen and the other group in an open pasture. After the cows reach adulthood, she wants to compare the weights of the two groups. The data passed all parametric assumptions.

b. She randomly divides her sample into two even groups and raises one group in the pen and the other group in an open pasture. When they reach adulthood, she records their weights as either “healthy” or “undernourished.”

c. She knows that an average adult cow should weigh 1,300 pounds. So she raises all 40 cows in the small pen and measures their weight once they reach adulthood. Although the raw weight measurements were not normally distributed, the log-transformed weights pass the normality assumption.