Part 1: Determining and Interpreting a "Margin of Error"

(1) Interpret, in your own words, what is meant by a "margin of error of plus or minus percentage 3 percentage points " and what is meant by " a statistical tie."

(2) What kind of statistical test is appropriate for determining the confidence interval for such a survey? Explain.

(3) Use you graphing calculator to assess the accuracy of the newspaper article's statement about the margins of error for these samples. Was the newspaper reporting accurate? What unreported confidence level was used to determine the margin of error? [95%]

(4) Again interpret "margin of error," this time incorporating the confidence level.

(5) Predict what the "margin of error" would be for this proportion of voters at the 99% confidence level. Calculate the "margin of error" for the 99% confidence levels, and discuss your prediction. In general, discuss how a survey's margin of error is related to the confidence level chosen.

(6) The survey reported in the newspaper was based on samples of 1218 and 999 respondents. Discuss the appropriateness of this sample size for obtaining reliable results in a presidential election.

(7) Predict what the 95% confidence level "margin of errors" would be for surveys, with the same proportion, but with sample sizes of n=100, 200, 500, 1000 and 10,000.

(8) Use your calculator to find the margins of error for these samples.

(9) Discuss your predictions, and the gains and trade-offs involved with various sample sizes. Discuss reasonable sample sizes for presidential elections.

(10) Write the general expression for the standard error for this distribution. Examine this expression and predict the shape of the graph of this standard error as a function of sample size. Discuss how this predicted shape is consistent with the results found for Task 8.

(11) Using the proportion for Gore and the 95% confidence level, graph the standard error as a function of sample size, and trace along the graph. Compare your observations with the results found in Task 8.

(12) Predict the position of the graph of the 99% standard error as a function of sample size.

(13) On the same screen, graph the 99% confidence level standard error as a function of sample size. Discuss your observations.

Part 3: The Effect of Proportion on Confidence Intervals

Extension 1: The 2000 Presidential Primaries

An earlier Dartmouth College-Associated Press poll conducted by during the 2000 presidential primary season yielded the following data. For the Republicans, Senator John McCain received 42% and Governor George W Bush received 33% of the votes from a sample of 518 likely voters. For the Democrats, Vice President Gore received 48% and former Senator Bradley received 41% of the votes cast by 418 likely voters. The newspaper reported margins of error of 4.5 and 5 percentage points, respectively. Comment on these numbers.