Mathematics

Psychology: Training Rats  The following data are based on information from the Regis University Psychology Department. In an effort to determine if rats perform certain tasks more quickly if offered larger rewards, the following experiment was performed. On day 1, a group of three rats was given a reward of one food pellet each time they ran a maze. A second group of three rats was given a reward of five food pellets each time they ran the maze. On day 2, the groups were reversed, so the first group now got five food pellets for running the maze and the second group got only one pellet for running the same maze. The average times in seconds for each rat to run the maze 30 times are shown in the following table.

Rat A B C D E F
Time with one food pellet 3.6 4.2 2.9 3.1 3.5 3.9
Time with five food pellets 3 3.7 3 3.3 2.8 3

Do these data indicate that rats receiving larger rewards tend to run the maze in less time? Use a 5% level of significance.

Atlantis is a small, isolated island in the South Atlantic. The inhabitants grow potatoes and catch fresh fish. The accompanying table shows the maximum annual output combinations of potatoes and fish that can be produced. Obviously, given their limited resources and available technology, as they use more of their resources for potato production, there are fewer resources available for catching fish. a. Draw a production possibility frontier with potatoes on the horizontal axis and fish on the vertical axis illustrating these options, showing points A–F. b. Can Atlantis produce 500 pounds of fish and 800 pounds of potatoes? Explain. Where would this point lie relative to the production possibility frontier? c. What is the opportunity cost of increasing the annual output of potatoes from 600 to 800 pounds? d. What is the opportunity cost of increasing the annual output of potatoes from 200 to 400 pounds? e. Can you explain why the answers to parts c and d are different?

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