A table represents the number of students who passed or failed an aptitude test at two different campuses.East Campus West CampusPassed 48 37Failed 52 63In order to determine if there is a significant difference between campuses and pass rate, the chi-square test for association and independence should be performed.What is the expected frequency of West Campus and failed?50 students63 students50.7 students57.5 students
Question
A table represents the number of students who passed or failed an aptitude test at two different campuses.East Campus West CampusPassed 48 37Failed 52 63In order to determine if there is a significant difference between campuses and pass rate, the chi-square test for association and independence should be performed.What is the expected frequency of West Campus and failed?50 students63 students50.7 students57.5 students
Solution
To calculate the expected frequency for the West Campus and failed students, we need to follow these steps:
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Calculate the total number of students who failed, regardless of the campus. This is 52 (from East Campus) + 63 (from West Campus) = 115.
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Calculate the total number of students at West Campus, regardless of whether they passed or failed. This is 37 (passed) + 63 (failed) = 100.
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Calculate the total number of students in both campuses. This is 48 (passed at East) + 52 (failed at East) + 37 (passed at West) + 63 (failed at West) = 200.
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The expected frequency is then (total failed * total at West Campus) / total students = (115 * 100) / 200 = 57.5 students.
So, the expected frequency of students who failed at West Campus is 57.5 students.
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