3. A farmer wants to study the effect of letting her Holstein cows, Bos Taurus, roam...

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3. 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). All relevant assumptions are confirmed for each scenario. (2pt each) 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 measures the weight of each cow in pounds. 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 weights in pounds once they reach adulthood. She wants to know if her cows have a healthy weight, on average. 3. 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). All relevant assumptions are confirmed for each scenario. (2pt each) 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 measures the weight of each cow in pounds. 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 weights in pounds once they reach adulthood. She wants to know if her cows have a healthy weight, on average.