Confidence Intervals and Errors:
An opinion poll asks 1500 randomly chosen United States residents their opinions
about relations with the nations of Europe. The announced margin of error for 95%
confidence is + 3 points. But some people were not on the list from which
respondents were chosen, some could not be contacted, and some refused to answer.
Does the announced margin of error include errors from these causes? Explain
your answer.
The announced margin of error for a confidence interval represents the error that arises due to the sampling process. In this case, the announced margin of error is + 3 points. It is important to note that this margin of error only takes into account the variability introduced by the sampling process.
The sampling process involves randomly selecting 1500 United States residents to participate in the opinion poll. However, it is inevitable that some individuals will be missed or cannot be reached, and some may refuse to answer. These are known as non-sampling errors, which are different from the sampling errors that the margin of error accounts for.
Non-sampling errors can arise due to various factors, such as incomplete coverage of the target population, non-response bias, or measurement errors. These errors are not reflected in the announced margin of error. Therefore, the margin of error does not include errors from these causes.
While the announced margin of error provides a measure of uncertainty based on the sampling process, it does not account for potential biases and errors introduced by non-sampling issues. It is important to consider these sources of error when interpreting the results of the opinion poll.