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(a)
To design an experiment that will require a two sample t procedure to analyse the results.
(a)
Explanation of Solution
In the question researchers want to see if people can work as effectively with as without distraction as some students do homework with the TV on. They will run the random experiment b two ways: first when the room will be quiet and the second in the same room when a TV will be on, tuned to MTV. Thus, to design an experiment that will require a two sample t procedure to analyse the results we have to randomly assign half of the volunteers to the group with the quiet room. And the remaining volunteers assigned to the group with the TV. And then we will compare the mean completion time of the two groups.
(b)
To design an experiment that will require a matched-pairs t procedure to analyse the results.
(b)
Explanation of Solution
In the question researchers want to see if people can work as effectively with as without distraction as some students do homework with the TV on. They will run the random experiment b two ways: first when the room will be quiet and the second in the same room when a TV will be on, tuned to MTV. Thus, to design an experiment that will require a matched-pairs t procedure to analyse the results, we have all volunteers will do the experiment twice. And half of the volunteers will first complete puzzles in a quiet room and then in the room with the TV. And the other half of the volunteers will first complete puzzles in the room with the TV and then in the quiet room. And then we will compare the difference in completion time for each volunteer.
(c)
To explain which experiment would you consider the stronger design and why.
(c)
Answer to Problem 2E
The matched pair design is considered to be stronger.
Explanation of Solution
In the question researchers want to see if people can work as effectively with as without distraction as some students do homework with the TV on. They will run the random experiment b two ways: first when the room will be quiet and the second in the same room when a TV will be on, tuned to MTV. Thus, by looking at the two designs in the above part (a) and (b), that is to design an experiment that will require a two sample t procedure to analyse the results and second one to design an experiment that will require a matched-pairs t procedure to analyse the results, we can say that we would consider the design of the matched pairs the stronger design because in this case the comparisons are between two groups who contain the same subjects each, while the groups for the two-sample t procedure are different and thus the variation between the two groups will be worse in the two-sample t procedure.
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