Preliminary Data Analyses Indicate That You Can Reasonably Consider the Assumptions

Preliminary data analyses indicate that you can reasonably consider the assumptions for using pooled t-proceduressatisfied. Perform the required hypothesis test by using either the critical-value approach or the P-value approach asindicated.
-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. $$\begin{array} { r | r } \text { College A } & \text { College B } \\ \hline 3.7 & 3.82 .8 \\ 3.2 & 3.24 .0 \\ 3.0 & 3.03 .6 \\ 2.5 & 3.92 .6 \\ 2.7 & 3.84 .0 \\ 3.6 & 2.53 .6 \\ 2.8 & 3.9 \\ 3.4 & \end{array}$$ 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. $\left( \text { Note: } \bar { x } _ { 1 } = 3.1125 , \bar { x } _ { 2 } = 3.4385 , s _ { 1 } = 0.4357 , s _ { 2 } = 0.5485 . \right)$

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Critical values Do not reject . At th...

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