Statistics Final Review Questions Only 1 Question Please Help?

Question by Scott: Statistics Final Review Questions only 1 question please help?
6.In a survey conducted by researchers at the University of Wisconsin, subjects were asked the question “Have you ever used cocaine?” in one of three methods, anonymous survey, personal interview, or phone survey. The contingency table below shows the results of this survey of 2400 students. Suppose one subject is randomly selected from this group. Answer each of the following.

Survey Method NO YES TOTAL
Anonymous 576 224 800
Personal 600 200 800
Phone 632 168 800
Total 1808 592 2400

1.0.247
2.0.28
3.0.25
4.0.21
5.No
6.Yes
7.0.093
8.0.083
9.0.07

Using (1-9) use each only once
A.What is the probability that the subject answered Yes?
B.What is the probability that the subject answered Yes given that it was an Anonymous
interview?
C.What is the probability that the subject answered Yes given that it was a Personal interview?
D.What is the probability that the subject answered Yes given that it was a Phone interview?
E.Based on these results, does it appear that the response is independent of type of interview?

Best answer:

Answer by Weff
A. Probability of an event is number of cases when event happens divided by all cases. So, to calculate probability we need to divide total “YES” answers by total cases. 592/2400=0.247. The answer is (1).

B. This is a bit more complicated case. We have 2 events, and the 2nd even can only happen IF 1st one happened. I mean you can calculate “YES” probability ONLY if it was Anonymous interview.
This is “complicated event” and probability theory says that probability of each event multiples in this case.
So, let’s count probability if it was Anonymous interview. It’s obvious that it’s 1/3, because we have only 3 variations. Probability of “YES” answer is 224/800=0.28. And so probability of complicated event is 0.28/3=0.093. The answer is (7)

C. Same case that in B, only the numbers different. Probability of Personal interview is same 1/3 and probability of “YES” answer is 200/800=0.25. So, totally 0.25/3=0.083. The answer is (8)

D. Same 1/3 and 168/800=0.21. 0.21/3=0.07. The answer is (9).

E. Here we must analyze probabilities of “YES” answers in Anonymous, Personal and Phone interview. We’ve done that before, so we have: 0.28, 0.25, 0.21. We see, that probability of “YES” answer is more in Anonymous survey, less in Personal survey and smallest in Phone survey.
That means that response depends of type of interview. So it is, there are not so many people ready to answer truth on such question by phone 🙂
The answer is (5)

Add your own answer in the comments!

Sentencing reform overdue

Filed under: statistics on cocaine

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