Perform the Indicated Hypothesis Test Use a 010 Significance Level to Test the Claim That the Mean

Perform the indicated hypothesis test. Assume that the two samples are independent simple random samples selected from normally distributed populations. Also assume that the population standard deviations are equal (?1 = ?2), so that the standard error of the difference between means is obtained by pooling the sample variances .
-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. $$\begin{array} { c | c c } \text { College A } & \text { College B } \\\hline 3.7 & 3.8 & 2.8 \\3.2 & 3.2 & 4.0 \\3.0 & 3.0 & 3.6 \\2.5 & 3.9 & 2.6 \\2.7 & 3.8 & 4.0 \\3.6 & 2.5 & 3.6 \\2.8 & 3.9 & \\3.4 & &\end{array}$$
Use a 0.10 significance level to test the claim that the mean GPA of students at college A is equal to the mean GPA of students at college B. Use the traditional method of hypothesis testing. $$\text { (Note: } \bar { x } _ { 1 } = 3.1125 , \bar { x } _ { 2 } = 3.4385 , \mathrm {~s} _ { 1 } = 0.4357 , \mathrm {~s} _ { 2 } = 0.5485 . \text { ) }$$