Question
Table 1 Videogames and GPA
Student brought videogame Roommate brought videogame Sample size Mean GPA St. Dev. No No Yes No No Yes Yes Yes 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 equals 210 first-year students who were randomly assigned a roommate. Table 1 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. Considering only students who do bring a videogame to campus, find a 99% confidence interval for the difference in mean GPA between students whose roommate does not bring a videogame and those whose roomate does bring a videogame mu Subscript Upper N Baseline minus mu Subscript Upper Y , where mu Subscript Upper N represents the mean GPA for students whose roommate does not bring a videogame and mu Subscript Upper Y represents the mean GPA for students whose roommate does bring a videogame.
Explanation / Answer
Roommate does not bring a videogame
n=44
mean=3.039
sd=0.689
Roommate does bring a videogame
n=40
mean=2.754
sd=0.639
Calculations
Population 1 Sample Degrees of Freedom
43
Population 2 Sample Degrees of Freedom
39
Total Degrees of Freedom
82
Pooled Variance
0.4431
Standard Error
0.1454
Difference in Sample Means
0.2850
Confidence Level
99%
Intermediate Calculations
Degrees of Freedom
82
t Value at 99%
2.6371
Interval Half Width
0.3835
Confidence Interval
Interval Lower Limit
-0.0985
Interval Upper Limit
0.6685
99% confidence interval for the mean difference = (-0.0985, 0.6685)
Calculations
Population 1 Sample Degrees of Freedom
43
Population 2 Sample Degrees of Freedom
39
Total Degrees of Freedom
82
Pooled Variance
0.4431
Standard Error
0.1454
Difference in Sample Means
0.2850