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Chapter 4: Problem 93

\(A\) farmer is conducting an experiment to determine which variety of apple tree, Fuji or Gala, will produce more fruit in his orchard. The orchard is divided into 20 equally sized square plots. He has 10 trees of each variety and randomly assigns each tree to a separate plot in the orchard. What are the experimental unit(s) in this study? (a) The trees (c) The apples (e) The orchard (b) The plots (d) The farmer

Short Answer

Expert verified
The experimental units are the plots.

Step by step solution

01

Identifying the Experiment Design

The experiment aims to determine the fruit production of two apple tree varieties. The farmer has 20 square plots and assigns one tree to each plot, spread over 10 Fuji and 10 Gala apple trees.
02

Defining an Experimental Unit

An experimental unit is the smallest division of a study such that each unit receives one treatment condition. In this experiment, each plot is arranged to contain one tree of either Fuji or Gala.
03

Selecting the Correct Experimental Unit

Each plot is treated independently, receiving either a Fuji or Gala tree. Since each plot can vary in output individually and is the smallest group to receive a treatment, the experimental units in the experiment are the plots.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Experimental Units
In any scientific study or experiment, it is crucial to identify the experimental units. An experimental unit is the smallest division in a study that can receive a specific treatment or condition.
  • In the context of our apple tree example, the plots of land are considered the experimental units.
  • Each plot receives one apple tree, either Fuji or Gala.
  • This setup ensures that each plot can be independently analyzed for fruit production.
Simplifying the concept: Think of experimental units as individual containers, each needing to receive a unique ingredient or treatment. Here, each plot hosts its own variety of apple tree. This has the benefit of clarity, as it helps segregate different conditions applied to the study, facilitating straightforward data analysis.
Random Assignment
Random assignment is a fundamental step in experimental design that ensures the treatment groups are comparable. It involves randomly allocating the experimental units to different treatment groups to limit the impact of confounding variables. This randomness helps establish a fair baseline to measure the effect of the treatment.
  • In our apple tree experiment, each of the 20 plots was assigned either a Fuji tree or a Gala tree at random.
  • This random allocation is essential to ensure the differences in plot conditions do not favor one type of apple tree over the other.
Imagine this step as drawing names from a hat to create fair teams in a game. Here, the trees are distributed randomly across the plots to ensure unbiased results, which enhances the experiment's reliability.
Controlled Experiment
A controlled experiment involves a deliberate manipulation of one or more variables while keeping other variables constant. This allows researchers to isolate and determine the effect of the manipulated variable.
  • In our experiment, the variable of interest is the type of apple tree, Fuji or Gala.
  • The farmer controls other factors, such as plot size and soil conditions, ensuring that any variation in fruit production can be attributed mainly to the tree type rather than the environment.
Think of a controlled experiment as baking a cake where only the flavor of frosting differs each time. The base cake is consistent, letting you focus on how each frosting variant changes the overall taste.
Statistical Study Design
The design of a statistical study is a blueprint for how to conduct an investigation. It lays out how data will be collected, controlled, and analyzed.
  • The farmer sets up his orchard experiment by defining plots and randomly assigning apple trees, adhering to a structured plan.
  • Key aspects in this design include defining experimental units, ensuring random assignment, and applying control techniques.
  • This methodology fosters clear and reliable conclusions about which apple tree variety yields more fruit.
Imagine statistical study design as crafting a roadmap for a journey. The farmer's plan thoughtfully considers each step鈥攆rom selecting plots to analyzing fruit output鈥攕etting the path for clear and insightful results.

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Most popular questions from this chapter

Identify the experimental units, the explanatory and response variables, and the treatments. Ability to grow in shade may help pines found in the dry forests of Arizona to resist drought. How well do these pines grow in shade? Investigators planted pine seedlings in a greenhouse in either full light, light reduced to \(25 \%\) of normal by shade cloth, or light reduced to \(5 \%\) of normal. At the end of the study, they dried the young trees and weighed them.

A lumber company wants to estimate the proportion of trees in a large forest that are ready to be cut down. They use an aerial map to divide the forest into 200 equal-sized rectangles. Then they choose a random sample of 20 rectangles and examine every tree that's in one of those rectangles. (a) What is the name for this kind of sampling method? (b) Give a possible reason why the lumber company chose this method.

A football coach hears that a new exercise program will increase upper-body strength better than lifting weights. He is eager to test this new program in the off-season with the players on his high school team. The coach decides to let his players choose which of the two treatments they will undergo for 3 weeks - exercise or weight lifting. He will use the number of push-ups a player can do at the end of the experiment as the response variable. Which principle of experimental design does the coach's plan violate? Explain how this violation could lead to confounding.

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