Test the Indicated Claim About the Means of Two Populations $\left. \bar { x } _ { 1 } = 3.1125 , \bar { x } _ { 2 } = 3.4385 , s _ { 1 } = 0.4357 , s _ { 2 } = 0.5485 . \right)$

Essay

Test the indicated claim about the means of two populations. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal.

Use a 0.10 significance level to test the claim that the mean GPA of students at college A is different from the mean GPA of students at college B.
(Note: $\left. \bar { x } _ { 1 } = 3.1125 , \bar { x } _ { 2 } = 3.4385 , s _ { 1 } = 0.4357 , s _ { 2 } = 0.5485 . \right)$
Include your null and alternative hypotheses, the test statistic, p -value or critical value(s), conclusion about the null hypothesis, and conclusion about the claim in your answer.