A researcher was interested in comparing the GPAs of students at the University of Toronto Scarborough and Mississauga campuses.Independent random samples of 8 students from the Scarborough campus and 13 students from the Mississauga campus yielded the following GPAs. $$\begin{array} { c | c c }
\text { Scarborough } & \text { Mississauga } \
\hline 3.7 & 3.8 & 2.8 \
3.2 & 3.2 & 4.0 \
3.0 & 3.0 & 3.6 \
2.5 & 3.9 & 2.6 \
2.7 & 3.8 & 4.0 \
3.6 & 2.5 & 3.6 \
2.8 & 3.9 & \
3.4 & &
\end{array}$$ Determine a 95% confidence interval for the difference, $\mu _ { 1 } - \mu _ { 2 } ,$ between the mean GPA of all students at the Scarborough campus and the mean GPA of all students at the Mississauga campus.
A)(-0.70,0.05)
B)(-0.81,0.15)
C)(-0.75,0.10)
D)(-0.13,0.78)
E)(-0.78,0.13)

Question

A researcher was interested in comparing the GPAs of students at the University of Toronto Scarborough and Mississauga campuses.Independent random samples of 8 students from the Scarborough campus and 13 students from the Mississauga campus yielded the following GPAs. $$\begin{array} { c | c c } 
\text { Scarborough } & \text { Mississauga } \
\hline 3.7 & 3.8 & 2.8 \
3.2 & 3.2 & 4.0 \
3.0 & 3.0 & 3.6 \
2.5 & 3.9 & 2.6 \
2.7 & 3.8 & 4.0 \
3.6 & 2.5 & 3.6 \
2.8 & 3.9 & \
3.4 & &
\end{array}$$ Determine a 95% confidence interval for the difference, $\mu _ { 1 } - \mu _ { 2 } ,$ between the mean GPA of all students at the Scarborough campus and the mean GPA of all students at the Mississauga campus.
A)(-0.70,0.05)
B)(-0.81,0.15)
C)(-0.75,0.10)
D)(-0.13,0.78)
E)(-0.78,0.13)

Quizplus · Accepted Answer

The confidence interval is calculated using the means and standard deviations of the two samples, and option E is the correct interval for the difference in means.

A Researcher Was Interested in Comparing the GPAs of Students