Mrs. Orlof teaches two history classes, one in the morning and one in the afternoon. Yesterday she gave the same test to both classes. Anyone who failed the test must take a retest. Since a greater percentage of students who took the morning test failed the test than students who took the afternoon test, more of Orlof’s morning history students than afternoon history students will have to take the retest.
The conclusion above is not necessarily valid because
A larger percentage doesn't mean more students. The morning class may be larger than the afternoon class.
the conclusion is based on a comparison of the percentage of students who failed the test in the morning class with the percentage of students who failed in the afternoon class. However, the total number of students in each class is not taken into account.
To determine the validity of the conclusion, we would need to know the total number of students in each class and compare the actual number of students who failed the test in the morning class with the actual number of students who failed in the afternoon class. Only then can we determine if more morning students will have to take the retest.
So, without further information about the total number of students in each class and the actual number of students who failed the test, we cannot say for certain whether the conclusion is valid.