A questionnaire was mailed to 1000 registered municipal...

A questionnaire was mailed to 1000 registered municipal voters selected at random. Only 500 questionnaires were returned, and of the 500 returned, 360 respondents were strongly opposed to a surcharge proposed to support the city Parks and Recreation Department. Are you willing to accept the $72 \%$ figure as a valid estimate of the percentage in the city who are opposed to the surcharge? Why or why not?

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Key Concepts

Random Sampling

Random sampling is a selection process where every member of the population has an equal chance of being chosen. It is essential for reducing selection bias and ensuring that the sample is initially representative of the overall population.

Nonresponse Bias

Nonresponse bias occurs when individuals selected for the sample do not respond, and those who do respond differ systematically in their opinions or characteristics from those who do not. In this case, only 500 of 1000 voters responded, which may lead to biased estimates if the nonrespondents had different views on the surcharge.

Representativeness

Representativeness refers to how well the sample reflects the true characteristics of the overall population. A low response rate calls into question whether the respondents accurately represent all municipal voters, potentially compromising the validity of the 72% opposition figure.

Survey Response Rate

The survey response rate is the proportion of those contacted who actually provide feedback. A low response rate, such as the 50% observed here, can weaken the reliability of the results since it increases the risk that the findings do not accurately capture the opinions of the entire targeted population.

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