Public opinion polls are taken on a wide range of topics, but polls are known to have a margin of error. In particular the Gallup organization states Results are based on telephone interviews with 1,000 national adults, aged 18 and older .... For results based on the total sample of national adults, one can say with 95% confidence that the maximum margin of sampling error is 3 percentage points. In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls. In this exercise we will use Monte Carlo simulation to investigate these claims. Assume that the probability that a randomly selected individual supports a position with 50% probability.

In this problem we will use R to recreate this analysis. Note: you must demonstrate the use of R to receive credit. Do the following: Sample from a binomial random variable to represent the poll. The variable should have n = 1,000 and p=.5. Calculate the proportion success as the number of success and calculate the error as the difference between the simulated proportion and the true proportion of 50%. Report the mean and standard deviation of the proportion supporting 1 Report the mean and the standard deviation of the error Calculate the Margin of Error for the 95% Confidence Interval (i.e. half the difference between the 2.5th and 97.5th percentile.) Now run sensitivity analysis that varies the number of respondents from 100 to 2,000. Calculate and plot the MOE. Paste the graph in the template. Run a second sensitivity analysis that runs the true proportion from 10% to 90% with n at 1,000. Plot that MOE and paste it into the template. Past your R code into the template.