Considering only students whose roommate does bring a videogame to campus, find and interpret a 95% confidence interval for the difference in mean GPA between students who bring a videogame and those who do not bring a videogame. Comment on the effect on these students of bringing a videogame.

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? Exercise B.7 on page 306 introduces a study involving n = 210 first-year students who were randomly assigned a roommate. Table 6.19 gives summary statistics on grade point average (GPA) for the first semester depending on whether the student and/or the roommate brought a videogame to campus.

Table 6.19

Exercise B.7 on page 306

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 examining this question looked at n = 210 students entering Berea College as first-year students in the Fall of 2001 who were randomly assigned a roommate. The explanatory variable is whether or not the roommate brought a videogame to college and the response variable is grade point average (GPA) for the first semester.

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Student brought Roommate brought Std. Dev. Sample Size videogame videogame No Mean GPA 0.590 0.689 No Yes No Yes 88 3.128 No 44 3.039 Yes Yes 38 2.932 0.699 40 2.754 0.639