Mrs. Orlof Teaches Two History Classes, One In The Morning

Removed Mrs Orlof Teaches Two History Classes One In The Morning A

[removed] 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

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The argument presented suggests that because a higher percentage of students in the morning class failed the test compared to the afternoon class, there will be more students from the morning class needing to retake the test. However, this conclusion is not necessarily valid, as it overlooks several crucial factors related to the total number of students in each class and the actual number of students failing in each group.

Firstly, the percentage of students failing in each class is relative and does not consider the total number of students enrolled in each session. For instance, if the morning class had significantly more students than the afternoon class, a higher percentage of failures could still translate into a greater absolute number of students retaking the test. Conversely, if the morning class had fewer students, even a higher failure rate might result in fewer total students needing a retest compared to the afternoon class.

Secondly, the conclusion assumes that the difference in failure percentages directly correlates with the number of students retaking the test, without accounting for the actual class sizes. The failure percentage is a ratio that needs to be multiplied by the total number of students to derive the actual number of students failing. Without knowing the total number of students in each class, the assertion that more students will retake the test from the morning class cannot be conclusively made.

Moreover, the failure rate percentage itself may be influenced by the class composition, such as varying academic preparedness or different levels of motivation, which can affect the failure rate without necessarily indicating a larger number of failures in absolute terms. This means that a higher failure percentage might be disproportionately affecting a smaller class, resulting in fewer students needing the retest than in a larger class with a lower failure percentage.

Additionally, statistical principles highlight that percentage failure rates are not sufficient to determine exact numbers without knowing the sample sizes. These principles emphasize that to accurately predict the total number of students retaking the test, one must consider both the failure percentage and the total number of students enrolled in each class.

In conclusion, the critical flaw in the reasoning is the assumption that higher failure percentages automatically translate into a greater number of students retaking the test. This neglects the effect of class sizes and fails to provide the necessary data to compare absolute numbers. Therefore, the conclusion that more of Mrs. Orlof’s morning students will have to retake the test is not necessarily valid solely based on failure percentages.

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