Preliminary Data Analyses Indicate That You Can Reasonably Use Nonpooled

Preliminary data analyses indicate that you can reasonably use nonpooled t-procedures on the given data. Apply anonpooled t-test to perform the required hypothesis test, using either the critical-value approach or the P-value approachas indicated.
-A researcher was interested in comparing the GPAs of students at two different colleges. Independent simple random samples of 8 students from college A and 13 students from college B yielded the following GPAs. $$\begin{array} { c | c c } \text { College A } & \text { College B } \\ \hline 3.7 & 3.8 & 2.8 \\ 3.2 & 3.2 & 4.0 \\ 3.0 & 3.0 & 3.6 \\ 2.5 & 3.9 & 2.6 \\ 2.7 & 3.8 & 4.0 \\ 3.6 & 2.5 & 3.6 \\ 2.8 & 3.9 & \\ 3.4 & & \end{array}$$ At the 10% significance level, do the data provide sufficient evidence to conclude that the mean GPA of students at college A differs from the mean GPA of students at college B? Use the critical-value approach. $$\text { (Note: } \left. \bar { x } _ { 1 } = 3.1125 , \bar { x } _ { 2 } = 3.4385 , s _ { 1 } = 0.4357 , s _ { 2 } = 0.5485 . \right)$$