EXAMPLE 20 Margin of error: The famous “plus or minus 3 percentage points”

Hardly a day goes by without some new poll being published. Polls influence the choice of candidates and the direction of their policies, especially during election campaigns. For example, the Gallup Organization polled 1012 American adults, asking them, “Do you think there should or should not be a law that would ban the possession of handguns, except by the police and other authorized persons?” Of the 1012 randomly chosen respondents, 374 said that there should be such a law.

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  1. Check that the conditions for the interval for have been met.
  2. Find and interpret the margin of error .
  3. Construct and interpret a 95% confidence interval for the population proportion of all American adults who think there should be such a law.

Solution

The sample size is . The observed proportion is , so

  1. We next check the conditions for the confidence interval. There are successes and failures. Because neither is less than 5, the conditions are met.

  2. The confidence level of 95% implies that our equals 1.96 (from Table 8.1). Thus, the margin of error equals

    We can estimate the population proportion of all Americans who think that there should be such a law to within with 95% confidence.

  3. The 95% confidence interval is

Note: Here we see the “plus or minus 3 percentage points.”

Thus, we are 95% confident that the population proportion of all American adults who think that there should be such a law lies between 34% and 40%.

NOW YOU CAN DO

Exercises 21–32.