A TV poll A television news program conducts a call-in poll...

A TV poll A television news program conducts a call-in poll about a proposed city ban on handgun ownership. Of the 2372 calls, 1921 oppose the ban. The station, following recommended practice, makes a confidence statement: “81% of the Channel 13 Pulse Poll sample opposed the ban. We can be 95% confident that the true proportion of citizens opposing a handgun ban is within 1.6% of the sample result.” (a) Is the station’s quoted 1.6% margin of error correct? Explain. (b) Is the station’s conclusion justified? Explain.

A TV poll A television news program conducts a call-in poll about a proposed city ban on handgun
ownership. Of the 2372 calls, 1921 oppose the ban. The station, following recommended practice, makes a confidence statement: “81% of the Channel 13 Pulse Poll sample opposed the ban. We can be 95%
confident that the true proportion of citizens opposing a handgun ban is within 1.6% of the sample result.”
(a) Is the station’s quoted 1.6% margin of error correct? Explain.
(b) Is the station’s conclusion justified? Explain.

Key Concepts

Margin of Error

The margin of error quantifies the potential discrepancy between a sample statistic and the actual population parameter, typically calculated as the product of a critical value (e.g., z-score for a given confidence level) and the standard error. It reflects how much random sampling error one may expect and depends on factors like sample size and variability in the data. This concept is central in survey research as it helps indicate the precision of the estimate.

Confidence Interval

A confidence interval provides a range of values, based on sample data, that is believed to contain the true population parameter with a specified probability (such as 95 percent). It is constructed by taking the sample estimate and adding and subtracting a margin of error determined by the chosen level of confidence and the estimated variability. This statistical tool is crucial for understanding the uncertainty associated with sample estimates.

Sampling Bias

Sampling bias refers to systematic errors that occur when a sample is not representative of the overall population, often due to the method of sample selection. In contexts where participation is self-selected, such as call-in polls, the sample may overrepresent individuals with strong opinions or greater engagement, leading to biased estimates. This concept is imperative when interpreting survey results, as it challenges whether inferential statistics, like the margin of error and confidence intervals, accurately reflect the true population parameters.

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