(1 point) Determining the prevalence of illicit substance in society can be very
ID: 3040582 • Letter: #
Question
(1 point) Determining the prevalence of illicit substance in society can be very difficult. Simply looking at police records doesn't give the whole picture, and any surveys designed to determine usage are subject to all sorts of biases. In particular, if responding "yes" to a particular question carries with it a stigma or implication of guilt, thern many respondents will lie. To alleviate this issue, we can use a survey design which is based on conditional probability Suppose we want to estimate the proportion of the Helena population who have used marijuana within the last month. We select 4864 participants and ask them each to first privately draw a card from a standard 52-card deck. If they get a "club" they are asked to respond truthfully to the question "Have you used marijuana within the last month?" If they get any other suit they are asked to respond to the question "Does your phone number end in an odd digit?" The study is blinded in the sense that the researcher doesn't know which question the participant is answering Hence, participants are guaranteed anonymity and are more likely to be truthful in their responses. The researchers only get a "yes" or "no" answer from each respondent and don't know the actual results of the card draw (a) What is the probability of getting a club? (b) What is the probability of not getting a club? (c) What is the expected probability of a person's phone number ending in an odd digit? (d) What is the expected probability of a person's phone number not ending in an odd digit? (e) We don't know the probability that a Helena resident has used marijuana in the last month (that is what we want!), but from this study we know the probability of answering the marijuana question and the percent of participants that answered "yes". Assume that 4864 people are surveyed and 2068 of them say "yes". Use this information to fill in the entire table drew a club did not draw a club Total response = yes! 2068 response no Total 4864Explanation / Answer
a)P(club) =13/52 =1/4
bP(no club) =1-1/4 =3/4
c) P(phone ending in odd digit) =1/2 (as there are 5 odd and 5 even number for end digit)
d)P(nt end in odd digit) =1/2
e)
drew club not drew club total response yes 244 1824 2068 response no 972 1824 2796 total 1216 3648 4864Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.