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.
(a) Discuss one of the important strengths of the method of data collection.
(b) In conducting a test to see whetherGPAis lower on average for students whose roommate brings a videogame to campus, define the parameter(s) of interest and state the null and alternative hypotheses.
(c) The p-value for the test in part (b) is 0.036. What is the conclusion for a 5% significance level?
(d) We are interested in seeing how large the roommate effect is on GPA. A 90% confidence interval for μ_vˆ’ μ_nis (ˆ’0.315,ˆ’0.015), where μ_vis the average GPA for first-year students whose roommate brings a videogame to college andμn is the averageGPAfor first-year students whose roommate does not bring a videogame to college. Explain how you can tell just from the confidence interval which group has a higher average GPA. Interpret the confidence interval in terms of roommates, videogames, and GPA.
(e) The researchers also record whether the student him- or herself brought a videogame to college. We conduct the same test as in part (b), to see if having a roommate bring a videogame to college hurts GPA, for each of these groups separately. For the test for students who do not themselves bring a videogame to college, the p-value is 0.068. What is the conclusion, using a 5% significance level?
(f) For the test for students who themselves bring a videogame to campus, the p-value for the test is 0.026. What is the conclusion, again using a 5% significance level?
(g) Using the p-values in parts (e) and (f), for which group of students (those who bring a videogame or those who do not) does having a roommate bring a videogame have a larger effect on GPA? Does this match what you would expect? Explain.
(h) For students who bring a videogame to campus, a 90% confidence interval for μ_vˆ’ μ_nis (ˆ’0.526,ˆ’0.044). Interpret this confidence interval in context and compare the effect size to that found for all students in part (d).

(i) The summary statistics are in Table B.3. Comment on the effect on GPA of videogames at college in general.
(j) Describe at least one additional test you might conduct using the data summarized in Table B.3.

Transcribed Image Text:

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