(5) (10 points) Teacher A boasts of being a better teacher than Teacher B and points to their respective classes' performances on the common final, where 25 of Teacher A's 31 students passed, while 19 of Teacher B's 33 students passed. The two decide to test whether the data is statistically significant evidence of Teacher A's claim. > prop. test (x=c (19, 25) , n=c(33, 31) , alternative = "less") 2-sample test for equality of proportions with continuity correction data; c(19, 25) out of c (33, 31) X-squared = 2,9586, df = 1, p-value = 0.04271 alternative hypothesis: less 95 percent confidence interval: -1.00000000 -0. 01597787 sample estimates: prop 1 prop 2 0. 5757576 0. 8064516 a. (5 points) What conclusion do you reach? Explain why. b. Are the assumptions behind the test satisfied