ECON 140A Brooklyn College Polling and Sampling Econometrics Questions

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Economics

ECON 140A

Brooklyn College

ECON

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ECON 140A FALL 2020 Exam 1 Notes: 1. Show your work and justify all steps. You will lose points if your reasoning is incomplete. 2. Submit your answers in the order in which they are asked in a single pdf document on GauchoSpace. 3. Review your answers to ensure they can be read and understood by another person, especially if you handwrite them. Problem 1. You’ve been hired to conduct a poll to assess whether a ballot proposition is likely to pass. (a) State the four assumptions necessary for your poll to provide useful insight. (4 points) (b) Some media outlets have reported that supporters of the proposition may be ‘shy’ about expressing their support. If true, which of the assumptions for polling would be invalid? If true, would you be likely to overestimate or underestimate support for the proposition? (2 point) (c) You have two assistants helping you conduct the poll. The three of you have agreed on the number of voters to sample and the estimator. However, one assistant proposes sampling with replacement. The other proposes sampling without replacement. Which proposal will lead to a lower variance for our estimator? Explain (1 point) (d) Assume there are N registered voters of which s plan to vote in favor of the ballot proposition. What is the probability that the first person you sample plans to vote in favor of the ballot proposition? (2 points) (e) Again, assume there are N registered voters of which s plan to vote in favor of the ballot proposition. You plan to sample without replacement. What is the probability that the second person you sample plans to vote in favor of the ballot proposition? Are Y1 and Y2 independent? (2 points) Problem 2. New Caledonia is a French territory located in the Pacific Ocean. With your recent work on the state ballot behind you, you’ve been hired to conduct a poll to determine support for independence. Individuals in New Caledonia are in favor or against independence. Let yk represent the response of individual k from the population. Let yk be coded as follows,  0, if individual k is against independence yk = 1, if individual k supports independence Let p represent the proportion of the population in favor of independence. You plan to collect a random sample (with replacement) of size n, (Y1 , Y2 , . . . , Yn ). (a) Is yk a random variable? Explain. (1 point) (b) One of your colleagues proposes the following estimator p̂ = n1 estimator is unbiased. (Show and explain your steps). (3 points) Pn i=1 Yi . Show that this (c) From class we know that variance of Y1 is p(1 − p). Derive the variance of the estimator from part b. (3 points) (d) Can you compute the variance with your sample? If not, explain and propose an alternative that you can compute. (1 point) (e) Your client wishes to have a margin of error of 5 percent. Using 95 percent confidence and an assumed value of p = 0.5, calculate the sample size required for the margin of error. (1 point) (f) Unfortunately, you have already collected a sample of 200 responses. It’s now one month later, but you proceed by collecting a new sample of 185 responses. Your colleague proposes combining the samples to achieve your desired margin or error. Can you use the combined sample to obtain an unbiased estimate of the level of support on the day you conducted the first poll? Explain. (1 point) Problem 3. After much deliberation about how to conduct your poll to determine support for independence in New Caledonia, you decide to poll 2000 individuals. Of these, 860 respond in favor of independence and 1140 respond against. Using the estimator from the previous question you find that p̂2000 = 0.43. France will grant New Caledonia independence if more than 50 percent of the population vote in favor. (a) Using your survey results, compute a 99 percent confidence interval for p, the proportion of the population in favor of independence. (3 points) (b) Using the confidence interval you computed above, explain if you think it is likely that the population of New Caledonia will vote in favor of independence. (3 points) (c) In October 2020 a vote was held and 46.7 percent of the population voted against independence. Your client asks you how it is that this was outside your confidence interval? Explain why the population parameter might fall outside the interval you calculated. Assume full voter turnout and that the four assumptions for polling were valid for your poll. (3 points) Page 2
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Answers to Econometrics Questions

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Answers to Econometrics Questions
Problem 1
a. The four assumptions include the following.
i.

Sampling was done from the whole population that would take part during the
ballot proposition.

ii.

The study sample was selected randomly from the population being investigated.

iii.

All the select...


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