A group of students at a high school took a standardized test. The number of students who passed or failed the exam is broken down by those who did or did not eat breakfast in the following table. Determine whether eating breakfast and passing the test are independent by filling out the blanks in the sentence below, rounding all probabilities to the nearest thousandth Passed Failed Did Eat Breakfast 98 7 Didn't Eat Breakfast 56 29
To determine whether eating breakfast and passing the test are independent, we need to compare the proportion of students who passed the test among those who ate breakfast with the proportion of students who passed the test among those who did not eat breakfast.
The total number of students who ate breakfast is 98 + 7 = 105.
The total number of students who did not eat breakfast is 56 + 29 = 85.
The proportion of students who passed the test among those who ate breakfast is 98/105 ≈ 0.933.
The proportion of students who passed the test among those who did not eat breakfast is 56/85 ≈ 0.659.
If eating breakfast and passing the test were independent, the proportion of students who passed the test regardless of eating breakfast would be the same as the proportion who passed the test among those who ate breakfast. However, in this case, the proportion of students who passed the test is different among those who ate breakfast compared to those who did not eat breakfast.
Therefore, we can conclude that eating breakfast and passing the test are not independent.