Question

You have recently been hired as the head of political polling in the country of Forsythia, a country with a fairly large population. You recently performed a poll for the upcoming presidential election. There are two candidates; the incumbent candidate and the opposition candidate. You randomly polled some Forsythian voters to determine the likelihood of the incumbent winning. You asked voters if they plan to vote for the incumbent or the opposition in the upcoming election. If they say the opposition, you record a 0. If they say the incumbent, you record a 1. The following is the data you recorded: 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1 This election is very important to you. The result of the pending election could cost you your job. You are under qualified for your job, but best buds with the incumbent candidate. If she gets elected you should keep your job. You were once emotionally involved with the opposition candidate’s spouse so if they get elected, you will probably lose your job.

9. Is there a clear leader in this election? _______?

10. Should you feel you have job security? ________?

11. The people of Forsythia are upset by the large margin of error of the recent presidential election poll. In response you decide to perform a second poll with a 5% margin of error and a 95% confidence level. How many people would you need to poll to achieve this kind of margin of error?

A. 5^2 = 25

B. (0.95^2)/(0.5^2) = 361

C. 1/.05^2 = 400

D. 95^2 = 9025

12. In a press release to appease the masses you share with the public the number of constituents you will be polling in the new poll. State the number of people that will be polled in a complete sentence. 13 Before performing the 2nd poll you feel lazy and decide you only need a 7.5% margin of error with a 95% confidence level. You would need to poll __________ people.

Answer 1

Answer to the question)

9) there are 58 people who have voted you and 53 people who voted the opposition

so you become a clear leader here

10) Since there are more votes in your favor, there is job security for sure, but as there are issues with the opposition, there can be some sort of risk for sure. Hence there is less job security in this case

11)

P = proportion of favorable votes = 58/110 = 0.53

Margin of error ( E) = 5% = 0.05

Confidence level = 95% , for it Z = 1.96

.

Sample size ( n) = p*(1-p) * (Z/ E)^2

Sample size ( n) = 0.53*0.47 * (1.96/0.05)^2

n = 382.78 ~383

.

12) the total number of people that need to be sample for a margin of error of 5% must be 383 people

.

13)

if margin of error ( E) = 0.075

then n = 0.53*0.47*(1.96/0.075)^2

n = 170.12 ~171