Question

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 her 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 Y; denote the number of points scored on the exam by the ith student (0 <Y; < 100), let X; denote the amount of time that the student has to complete the exam (X; = 90 or 120), and consider the regression model: Y; = Bo + BiX; + Wi. (a) Explain what the term ui represents. Why will different students have different values of ui? (b) Explain why E(ui|X;) = 0 for this regression model. (c) Are the other assumptions among SLR.1-SLR.4 satisfied? Explain why. (d) The estimated model is Y; = 49+0.24X;. i. Based on the estimated model, predict the average score of students given 90 minutes. Repeat for 120 minutes and 150 minutes. ii. Compute the average predicted gain in score for a student who is given an additional 10 minutes on the exam.

Answer 1

consider the experiment provided in the exercise to measure the effect of time Pressure on exam scog The information from the exercise is written below: - 400 students take the same slom. 2. Some students have ao Ming to complete the ens 3; some slauderts have 120 ring to complete the exam " Geam times are assigned based on the flip off a com s. Dependent variable is written below: 1 Y = Points scored by the ith student, osY; 2100 6. Independent variable is written below: xi = Time to complete the exam by the ith student Xi = 90 &120 2. The regression mode is 7 = Bot ß, xy +U; o the Term i represents other factory that have an effect on an individual students cheam sor. for example, studying time vary with students, and varying aptitude calability possessed by different students.

b. Due ndent of to x sandon Since assignment us refresents . of to, le is indoset deviation from the ومدمه علم so &Cu) zo. Algo Pendent, then Eus(X)=0 since it and are inse 1. The assumption that : (x,,Y:), i=1,-. n are independente and identically distributed draws from their joint distribution is true if this year's students are views as random dorows from the population of students that take this clogs. The assumption that; large outlies are unlikely :/ tip and to have non zero firlite fourth proments true's The restricted values of Y, OLY £100 and x=908 The computation of Prediction and estimated gain I written beloo. 1d is i score crom The of for the averos complete the is computation of the Prediction student given 90 min to shown below: Ti = 49 +0:24 x 90 7016

pe corputation of the Poediction for give Stuckery Pelowo 120 the aug score of exam is os shown min to complete the =ua +0.24x120 =9918 . lete aug score of students given 150 enam is as shown below: min. to co y = 49+0.24x150 = 85 " for the The computation of the estimates gain a student who is given an addition 10 enam is calculates of followy! in sco ming y = 0.24 xd -0.24x10 = 2.4