drtrtre
Mar 17, 2010, 09:34 PM
There are 6421 students living in Colleges of Residence at a large University. University authorities investigating the use of P among college residents sample randomly 300 college residents and ask the question: “Have you ever used P?” There are 21 responses of YES.
(a) Write down your estimate for the percentage (or proportion) of college residents who have used P.
(1 mark)
There was concern among University authorities about the truth of the response to the question and the following year a different procedure was used. A random sample of 300 college residents was again selected and the following procedure was carried out
A. Roll an unbiased six-sided die, allowing no one else to observe the outcome.
B. (I) If die shows 1, toss a fair coin and answer truthfully YES or NO to the question “Have you thrown a head?”
(ii) If die shows any other number answer truthfully YES or NO to the question “Have you ever used P?”
With this procedure, each college resident responded with a single YES or NO answer. The tree diagram is as follows where θ is the proportion of YES responses to the substance question. The problem is to find θ.
(b) Copy the tree diagram adding the four missing probabilities. (1 mark)
(c) The authorities received 84 YES responses and 216 NO responses.
(I) Write down the probability of a response YES in terms of θ. (1 mark)
(ii) Hence find the estimate, θ, for the proportion of Year 13 students who have tried P. (1 mark)
(iii) Compare this value with that obtained in (a), stating your conclusion about the proportion who have tried P. (1 mark)
(a) Write down your estimate for the percentage (or proportion) of college residents who have used P.
(1 mark)
There was concern among University authorities about the truth of the response to the question and the following year a different procedure was used. A random sample of 300 college residents was again selected and the following procedure was carried out
A. Roll an unbiased six-sided die, allowing no one else to observe the outcome.
B. (I) If die shows 1, toss a fair coin and answer truthfully YES or NO to the question “Have you thrown a head?”
(ii) If die shows any other number answer truthfully YES or NO to the question “Have you ever used P?”
With this procedure, each college resident responded with a single YES or NO answer. The tree diagram is as follows where θ is the proportion of YES responses to the substance question. The problem is to find θ.
(b) Copy the tree diagram adding the four missing probabilities. (1 mark)
(c) The authorities received 84 YES responses and 216 NO responses.
(I) Write down the probability of a response YES in terms of θ. (1 mark)
(ii) Hence find the estimate, θ, for the proportion of Year 13 students who have tried P. (1 mark)
(iii) Compare this value with that obtained in (a), stating your conclusion about the proportion who have tried P. (1 mark)