In this exercise, we investigate answers to the questions: How much of an effect does your roommate have on your grades? In particular, does it matter whether your roommate brings a videogame to...

Extracted text: In this exercise, we investigate answers to the questions: How much of an effect does your roommate have on your grades? In particular, does it matter whether your roommate brings a videogame to college? A study was conducted involving n for the first semester depending on whether the student and/or the roommate brought a videogame to campus. 210 first-year students who were randomly assigned a roommate. Table 1 gives summary statistics on grade point average (GPA) Student Roommate brought videogame brought videogame Sample size Mean GPA St. Dev. No No 88 3.128 0.590 Yes No 44 3.039 0.689 No Yes 38 2.932 0.699 Yes Yes 40 2.754 0.639 Table 1 Videogames and GPA We consider the effect of neither student bringing videogames compared to both students bringing them. (a) Find a 90% confidence interval for the difference in means between students in rooms in which neither the student nor the roommate brings a videogame and students in rooms in which both the student and the roommate bring a videogame uy – Hy,where µy represents mean GPA for students for whom neither the student nor the roommate brings a videogame and Hy represents mean GPA for students for whom both the student and the roommate bring a videogame. Round your answers to three decimal places. The 90% confidence interval is i to i