Question

In: Statistics and Probability

14. An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm...

14. An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following result was obtained. (Please show the calculation process)

Did Well on Midterm

Did Poorly on Midterm

Studying for Exam

80

20

Went Bar Hopping

30

70

Referring to above table, what is the probability that a randomly selected student did well on the midterm and went bar hopping the weekend before the midterm?

15. What is the probability that a randomly selected student did well on the midterm or went bar hopping the weekend before the midterm?

16. Referring to above table, the events "Did Well on Midterm" and "Studying for Exam" are

  1. statistically dependent.
  2. statistically independent.

Solutions

Expert Solution

Did Well on Midterm Did Poorly on Midterm Total
Studying for Exam 80 20 100
Went Bar Hopping 30 70 100
Total 110 90 200

14. Probability that a randomly selected student did well on the midterm and went bar hopping the weekend before the midterm?

Answer : The number of students who did well and went bar hopping is 30.

p = 30/200

15. What is the probability that a randomly selected student did well on the midterm or went bar hopping the weekend before the midterm?

Answer : The number of students who did well or went bar hopping is 80+30+70 = 180.

p = 180/200

16. Referring to above table, the events "Did Well on Midterm" and "Studying for Exam" are

  1. Events A and B are independent if the equation P(A∩B) = P(A) P(B) holds true.
  2. statistically independent.

Events A and B are independent if the equation P(A∩B) = P(A) P(B) holds true.

P("Did Well on Midterm" and "Studying for Exam") =P("Did Well on Midterm") * P( "Studying for Exam")

80/200 =110/200 * 100/200

0.4 not equal to 0.275

Events "Did Well on Midterm" and "Studying for Exam" are statistically dependent.

Hope this will be helpful. Thanks and God Bless You :)

orchestra answered 2 years ago
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