Question

Recycle and Review Exercises 29-31 refer to the following setting. Does the color in which words are printed affect your ability to read them? Do the words themselves affect your ability to name the color in which they are printed? Mr. Starnes designed a study to investigate these questions using the 16 students in his AP Statistics class as subjects. Each student performed the following two tasks in random order while a partner timed his or her performance: (1) Read $32$words aloud as quickly as possible, and (2) say the color in which each of$32$ words is printed as quickly as possible. Try both tasks for yourself using the word list given.

Color words (4.2) Let's review the design of the study-

a. Explain why this was an experiment and not an observational study.

b. Did Mr. Stames use a completely randomized design a: randomizéd black design? Why do you think he choose this experimental design?

c. Explain the purpose of the ramdom assignment in the context of the study.

Here are the data from Mr. Stames's experiment. For each subject, the time to perform the Iwo tasks is given to the nearest second.

Short answer

(a) The reason for this is that each individual receives two treatments.so this is an experiment.

(b) Mr Stames use a completely randomized block design

(c) Where there is no random assignment, experience could be a confounding variable.

Step-by-step solution

Part (a) Step 1: Given Information

Given table is

We have to explain why this was an experiment and not an observational study .

Part (a) Step 2: Explanation

Individuals are given treatments in an experiment so that their reactions may be tracked.

An observational research seeks to collect data without interfering with the view they're looking at.

Experiment

The reason for this is that each individual receives two treatments (read words and say colours).

Part (b) Step 1: Given Information

The given table is

We have to determine did Mr. Stames use a completely randomized design a: randomizéd black design and why do you think he choose this experimental design .

Part (b) Step 2: Explanation

The reason for the randomized block design is that each subject received two treatments and so each subject constructs a block.

The other option (a truly randomized design) would need each participant to receive only one treatment, resulting in a cost of$2$

Part (c) Step 1: Given Information

The given table is

We have to explain the purpose of the ramdom assignment in the context of the study.

Part (c) Step 2: Explanation

When the effects of two variables on a response variable cannot be separated from one another, two variables are assumed.

To eliminate any potential confounding variations in the groups before the experiment might affect the output data, random assignment is employed to make various groups of persons as comparable as possible.

In this situation, the order in which the two treatments are mentioned is chosen at random to ensure that prior experience has no bearing on the outcome. They are more familiar with the list after the first treatment and are therefore more likely to get a better time on the second treatment. As a result, in situations where there is no random assignment, experience may be a confounding variable.