Coleman (1964) interviewed 3,398 schoolboys and asked them about their self-perceived membership in the "leading crowd." Their response was either yes, they were a member, or no, they were not. The same boys were also asked about their attitude concerning the leading crowd. In particular, they were asked whether membership meant that it does not require going against one's principles sometimes or whether they think it does. Here, the first response will be indicated by a 1 and the second will be indicated by a 0. The results were as follows:
|
Member?
|
Attitude
|
|
1
|
0
|
|
Yes
|
757
|
496
|
|
No
|
1071
|
1074
|
These values, divided by the sample size, 3,398, are called relative frequencies. For example, the relative frequency of the event (Yes, 1) is 757/3398. Treat the relative frequencies as probabilities and determine
(a) the probability that an arbitrarily chosen boy responds Yes,
(b) P(Yes|1),
(c) P(1|Yes),
(d) whether the response Yes is independent of the attitude 0,
(e) the probability of a (Yes and 1) or a (No and 0) response,
(f ) the probability of not responding (Yes and 1),
(g) the probability of responding Yes or 1.