Q:\"A professor decides to run an experiment to measure the effect of time press
ID: 1138107 • Letter: Q
Question
Q:"A professor decides to run an experiment to measure the effect of time pressure on final exam scores. He gives each of the 400 students in his course the same final exam, but some students have 90 minutes to complete the exam while others have 120 minutes. Each student is randomly assigned one of the examination times based on the flip of a coin. Let Yi denote the number of points scored on the exam by the ith student ( 0 less than or equl to Yi less than or equal to 100), let Xi denote the amount of time that the student has to complete the exam (Xi = 90 or 120), and consider the regression model Yi = Beta0 + Beta1 Xi + ui , E(ui) = 0 Which of the following are true about the unobservable ui ? "
there is no way to calculate it
ui represents factors other than time that influence the student's performance on the exam.
ui will be zero for all students because time spent studying is likely the only factor that affects exam performance.
All students will necessarily have the same value of ui because they are part of the same population.
Q:"A professor decides to run an experiment to measure the effect of time pressure on final exam scores. He gives each of the 400 students in his course the same final exam, but some students have 90 minutes to complete the exam while others have 120 minutes. Each student is randomly assigned one of the examination times based on the flip of a coin. Let Yi denote the number of points scored on the exam by the ith student ( 0 less than or equl to Yi less than or equal to 100), let Xi denote the amount of time that the student has to complete the exam (Xi = 90 or 120), and consider the regression model Yi = Beta0 + Beta1 Xi + ui , E( ui) = 0 The Least Squares Assumptions Reminder 1. The error term ui has conditional mean zero given Xi : Yi = Beta0 + Beta1 Xi + ui , i = 1,..., n where E (u|Xi)= 0; 2. Xi ,Yi, i = 1,..., n, are independent and identically distributed (i.i.d.) draws from their joint distribution; and 3. Large outliers are unlikely: Xi and Yi have nonzero finite fourth moments. Assuming this year's class is a typical representation of the same class in other years, are OLS assumption (2) and (3) satisfied?"
Only OLS assumption #3 is satisfied.
Neither OLS assumption #2 nor OLS assumption #3 is satisfied.
Only OLS assumption #2 is satisfied.
Both OLS assumption #2 and OLS assumption #3 are satisfied.
there is no way to calculate it
ui represents factors other than time that influence the student's performance on the exam.
ui will be zero for all students because time spent studying is likely the only factor that affects exam performance.
All students will necessarily have the same value of ui because they are part of the same population.
Q:"A professor decides to run an experiment to measure the effect of time pressure on final exam scores. He gives each of the 400 students in his course the same final exam, but some students have 90 minutes to complete the exam while others have 120 minutes. Each student is randomly assigned one of the examination times based on the flip of a coin. Let Yi denote the number of points scored on the exam by the ith student ( 0 less than or equl to Yi less than or equal to 100), let Xi denote the amount of time that the student has to complete the exam (Xi = 90 or 120), and consider the regression model Yi = Beta0 + Beta1 Xi + ui , E( ui) = 0 The Least Squares Assumptions Reminder 1. The error term ui has conditional mean zero given Xi : Yi = Beta0 + Beta1 Xi + ui , i = 1,..., n where E (u|Xi)= 0; 2. Xi ,Yi, i = 1,..., n, are independent and identically distributed (i.i.d.) draws from their joint distribution; and 3. Large outliers are unlikely: Xi and Yi have nonzero finite fourth moments. Assuming this year's class is a typical representation of the same class in other years, are OLS assumption (2) and (3) satisfied?"
Only OLS assumption #3 is satisfied.
Neither OLS assumption #2 nor OLS assumption #3 is satisfied.
Only OLS assumption #2 is satisfied.
Both OLS assumption #2 and OLS assumption #3 are satisfied.
Explanation / Answer
Answer 1:
Option B. The error term represents the variation in dependent variable that are not explained by the independent variable. Thus, other factors that affect the dependent variable.
Answer 2:
Option D. Both the OLS assumptions are satisfied. Assumption 2 states that error term has a population mean of zero which is satisfied and assumption 3 states that all independent variables are uncorrelated with the error term which is true.
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