A report on 171 volunteer students participating in an experiment where each was
ID: 3127063 • Letter: A
Question
A report on 171 volunteer students participating in an experiment where each was randomly assigned to one of three groups. One group was made to feel guilty, one group was made to feel angry, and the third group was not influenced. Immediately after reaching these emotional states, the students were asked to decide whether or not to spend lots of money to repair a very old car (not a “historic”/antique). The “stated” option was “spend the money to repair the car”. The following raw data was recorded:
Emotional State
Choose stated option C
Don’t choose stated option C’
Totals
Guilt
45
12
57
Anger
8
50
58
Neutral
7
49
56
Totals
60
111
171
If a single student is chosen at random, what is the probability that the student is in the “anger” emotional state?
Answer: ___________________________
If a single student is chosen at random, what is the probability that the student chooses the stated option, given that the student is in the “anger” state?
Answer: __________________________
Are the events “choose the stated option” and “anger” independent? Explain mathematically why or why not.
Emotional State
Choose stated option C
Don’t choose stated option C’
Totals
Guilt
45
12
57
Anger
8
50
58
Neutral
7
49
56
Totals
60
111
171
Explanation / Answer
A) TOTAL WE HAVE 171 STUDENTS
TOTAL STUDENTS WHO ARE ANGRY = 58
PROBABILITY THAT SELECTED STUDENT IS ANGRY = 58/171 = 0.339
B)probability that the student chooses the stated option, given that the student is in the “anger” state = 8/58 = 0.137
C) P ( A B ) = P ( A )* P ( B )
P ( A B ) = 8/58 = 0.137
P(A)*P(B) = (60/171)*(111/171) = 0.227
HENCE NOT EQUAL THERE FOR NOT INDEPENDENT
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