Professor Hsieh decides to run an experiment to measure the effect of time press

Question

Professor Hsieh decides to run an experiment to measure the effect of time pressure on final exam scores. He gives each of the 50 students in his course the same final exam, but some students have 90 minutes to complete the exam, while the others have 120 minutes. Each student is randomly assigned one of the examination times based on the flip of a coin (25 students will be assigned to the 90 minutes' group and vice versa). Let Y_i denote the test score of student i and let X_i denote the amount of time assigned to student i (X_i = 90 or 120). Consider the regression model Y_i = a + beta X_i + u_i. Explain why E[u_i|X_i] = 0 for this regression model. Instead of flipping a coin, Prof. Hsieh decides to assign 90 minutes to junior and 120 minutes to senior. Will this cause any problem? It is reasonable to assume that senior students have higher math ability in general as they might have completed more math-related courses. If so, will the assignment in (B) lead to upward or downward bias of OLS estimation?

Explanation / Answer

Solution:- Professor Hsieh conducted an experiment under controlled conditions.The above experiment is known as controlled experiment.

He conducted the experiment by gving extra time,based on the flip of a coin.

Here, out of 50 students 25 students will get 90 minutes and 25 students will get 120 minutes time.

Let us suppose thatYi denotes the score and Xi denotes the amount of time assigned to each student.

In the experiment, those who got 120 minutes time, in that some students who prepare hard and know all the answers, they can solve the problems so fastly when compared to others.For such type of students giving extra time is of no use.There wont be any effect on their marks if extra time alloted to them.

In such case, when the regression is run, the estimated effect could be negative or close to 0.As a result, it is impossible to estimate the effect of addditional time on test score cannot be determined correctly.

So, the conditional probability is zero.

2) Instead of flipping a coin, if professor assign 90 minutes to junoir and 120 minutes to seniors also the conditional probability becomes zero.

Generally, seniors have higher math abitlity than juniors, so seniors can solve very easily and fastly when compared to juniors, so it is impossible to estimate the effect on the score

If seniors know al the answers they can solve with in the given time, no extra time will be required to such students, in that case, if we run the regression it moves towards negative or some time positive(though It is positive)

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