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AP Statistics 3.5 Introduction to Experimental Design- FRQs - Exam Style Questions

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Question

Researchers are investigating the effectiveness of using a fungus to control the spread of an insect that destroys trees. The researchers will create four different concentrations of fungus mixtures: \(0\) milliliters per liter (ml/L), \(1.25\) ml/L, \(2.5\) ml/L, and \(3.75\) ml/L. An equal number of the insects will be placed into \(20\) individual containers. The group of insects in each container will be sprayed with one of the four mixtures, and the researchers will record the number of insects that are still alive in each container one week after spraying.

(a) Identify the treatments, experimental units, and response variable of the experiment.

  • Treatments:
  • Experimental units:
  • Response variable:
(b) Does the experiment have a control group? Explain your answer.
(c) Describe how the treatments can be randomly assigned to the experimental units so that each treatment has the same number of units.

Most-appropriate topic codes (CED):

• TOPIC 3.5: Introduction to Experimental Design — parts (a), (b), (c)
▶️ Answer/Explanation
Detailed solution

(a)

  • Treatments: The four different concentrations of the fungus mixture: \(0\) ml/L, \(1.25\) ml/L, \(2.5\) ml/L, and \(3.75\) ml/L.
  • Experimental units: The \(20\) individual containers, each containing an equal number of insects.
  • Response variable: The number of insects that are still alive in each container one week after spraying.

(b)
Yes, the experiment has a control group. The group of containers that will be sprayed with the mixture containing \(0\) ml/L of fungus serves as the control group. This is because this group is treated in the same way as all other groups but does not receive the active ingredient (the fungus). This provides a baseline to which the effects of the other fungus concentrations can be compared.

(c)
To randomly assign the treatments, we can use the following process:

  1. Label each of the \(20\) containers with a unique number from \(1\) to \(20\).
  2. Create \(20\) identical slips of paper. On five slips, write “\(0\) ml/L”. On another five slips, write “\(1.25\) ml/L”. On another five, write “\(2.5\) ml/L”, and on the final five, write “\(3.75\) ml/L”.
  3. Place all \(20\) slips of paper into a hat or a box and mix them thoroughly.
  4. For each container (from \(1\) to \(20\)), draw one slip of paper from the hat without replacement. Assign the treatment written on the slip to that container.

This process ensures that each treatment is assigned to exactly five containers, and the assignment is completely random.

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