Table 1 Videogames and GPA Student brought videogame Roommat

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.

Solution

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