Question

Radio and television stations often air controversial issues during broadcast time and ask viewers to indicate their agreement or disagreement with a given stand on the issue. A poll is conducted by asking those viewers who agree to call a certain 900 telephone number and those who disagree to call a second 900 telephone number. All respondents pay a fee for their calls. a. Does this polling technique result in a random sample? b. What can be said about the validity of the results of such a survey? Do you need to worry about a margin of error in this case?

Short answer

Explain the validity of the results and whether margin of error should be a concern in this case. Answer: No, the polling technique used by radio and television stations does not result in a random sample. This is because only those viewers who feel strongly about the issue and are willing to pay the call fee will participate, creating a self-selection bias. As a result, the validity of the survey results can be questionable and may not accurately represent the opinions of the entire population. In this case, focusing on identifying the potential biases and sources of unreliability is more beneficial than calculating the margin of error.

Step-by-step solution

a. Does this polling technique result in a random sample?

This polling technique does not result in a random sample. The main reason is that the respondents are self-selected, meaning that only those viewers who feel strongly about the issue and are willing to pay the call fee will participate in the poll. This self-selection bias can lead to an unrepresentative sample of the entire population, as it is likely that those who don't care about the issue or don't want to pay the fee will not participate.

b. Validity of the results and margin of error

Due to the self-selection bias mentioned earlier, the validity of the survey results can be questionable. The survey may not accurately represent the opinions of the entire population because it only includes the opinions of people who are motivated and willing to pay the fee to express their views. As for the margin of error, it is usually calculated based on the sample size and the response distribution in a random sample. However, since this polling technique does not result in a random sample, it may not be appropriate to calculate the margin of error for this survey. Instead, it would be more beneficial to focus on identifying the potential biases and sources of unreliability in the survey.