A politician has a new policy idea and wants to know how the public views it. Th
ID: 3274656 • Letter: A
Question
A politician has a new policy idea and wants to know how the public views it. They issue a survey to randomly selected individuals in their precinct, asking if respondents do or do not favor this policy. Suggest a model for the number of respondents who favor the policy. You should state what you are modeling as random, what distribution the corresponding random variables have, and what the relevant parameter(s) is for that model. You may assume that there are very many people living in the precinct so that your model does not need to consider finite population sampling. What is the parameter space of your model? Which of the following quantities are statistics? (a) The response of the first person (b) The number of people in the precinct who favor the policy c) The number of respondents who favor the polivyExplanation / Answer
1. Here Binomial distribution best describes the data. Let X be number of persons who favor the policy.
Hence, X ~ Bin(n, p). Here 'n' and 'p' are the parameters of the model.
In this case n = total number of persons, p = probability that a respondent will favor the policy. (Ans).
2. Parameter space of n and p are the list of values they can obtain.
n = total number of persons = 1,2,......, 0 < p < 1. (Ans).
3. Statistic is measured only for sample. The response of the first person is from sample and also the number of respondents who favor the policy is from sample. So, (a) and (c) are statistics. (Ans).