SOLUTION: Krissy wanted to understand whether grade level had any relationship to their opinion on extending the school day. She surveyed some students and displayed the results in the table
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-> SOLUTION: Krissy wanted to understand whether grade level had any relationship to their opinion on extending the school day. She surveyed some students and displayed the results in the table
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Question 1012313: Krissy wanted to understand whether grade level had any relationship to their opinion on extending the school day. She surveyed some students and displayed the results in the table below:
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Let's add on the totals
In Favor
Opposed
Undecided
Total
Grade 9
6
2
7
15
Grade 10
5
11
8
24
Grade 11
12
15
11
38
Grade 12
17
5
13
35
Total
40
33
39
112
The row and column totals are found by adding up the values in each corresponding row or column. For example. The "15" in the first row of the column total (far right column) is found by adding up the values in the first row (6+2+7 = 15). The other totals are found the same way.
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Let's first compute P(Grade 11 | opposed)
P(Grade 11 | opposed) = (# in grade 11 AND who are opposed)/(# who are opposed)
P(Grade 11 | opposed) = 15/33
P(Grade 11 | opposed) = 5/11
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Now let's compute P(Opposed | Grade 11)
P(Opposed | Grade 11) = (# in grade 11 AND who are opposed)/(# who are in grade 11)
So the two expressions P(Grade 11 | opposed) and P(Opposed | Grade 11) are NOT the same value (5/11 is not equal to 15/38). This means that the two events being in grade 11 and being opposed are NOT independent. The two events are dependent.
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