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

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: $^{4} 81 \%$ 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." Is the station's conclusion justified? Explain.

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: $^{4} 81 \%$ 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." Is the station's conclusion justified? Explain.

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Key Concepts

Confidence Intervals

A confidence interval is a range derived from sample data that is used to estimate a population parameter with a certain level of confidence. It requires that the sample is representative of the population under study. When the assumptions of random sampling are met, the confidence interval accurately reflects the uncertainty inherent in the estimate.

Nonprobability Sampling and Sampling Bias

Nonprobability sampling, such as call-in polls, does not guarantee that every member of the population has an equal chance of being included. This introduces sampling bias, where the characteristics of those who choose to participate may differ systematically from those who do not, thereby undermining the validity of the inferences made from the sample.

Representativeness

Representativeness refers to the extent to which the characteristics of a sample mirror those of the overall population. When a sample is not randomly selected or is subject to self-selection bias, as in a call-in poll, the sample may not accurately reflect the views or traits of the entire population. This lack of representativeness can invalidate conclusions drawn about the population based on the sample data.

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