A psychologist wants to know if the difficulty of a task influences our estimate of how long we spend working at it. She designs two sets of mazes that subjects can work through on a computer. One set has easy mazes and the other has difficult mazes. Subjects work until told to stop (after $6$minutes, but subjects do not know this). They are then asked to estimate how long they worked. The psychologist has $30$students available to serve as subjects.

a. Describe an experiment using a completely randomized design to learn the effect of difficulty on estimated time. Make sure to carefully explain your method of assigning treatments.

b. Describe a matched pairs experimental design using the same $30$subjects.

c. Which design would be more likely to detect a difference in the effects of the treatments? Explain your answer.

Given: thirty students.

There are two treatments: easy maze and difficult maze.

Let us assign a unique number between to each student.

Use slips of paper, a random digit table or calculator to select 15 unique integers between . The corresponding students are then assigned to the easy maze.

The remaining students are assigned to hard maze.

We will then compare the estimates of the time worked among the two treatment groups.

Given: thirty students.

There are two treatments: easy maze and difficult maze.

Let us use two slips of paper, write “A” on one slip and “B” on other slip.

Put the slips face down on a table and shuffle them. Let each student randomly select one of the two slips and be sure to return and shuffle the slips around after each drawing. The students who selected the slip containing “A” will first execute the easy maze and then execute the difficult maze.

The students who selected the slip containing “B” will first execute the difficult maze and then execute the easy maze.

We will then compare the estimate of the time worked among the easy maze and the difficult maze.

Matched pairs would be more likely to detect the difference in the effects of the treatments because with one subject helps reduce the differences in the experiment. and this method is very effective in this case. And give the unbiased result of the survey.