Question

Radio and television stations often air controversial issues during broadcast time. A poll is then conducted, asking viewers who agree with the issue 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

#Short Answer The polling technique used by the radio and television stations does not result in a random sample and could lead to biased results. Therefore, the validity of the survey results may be questionable, and calculating a margin of error would not provide meaningful information in this case.

Step-by-step solution

Understanding random sampling

Random sampling is a technique used in statistics where each individual in the population has an equal chance of being selected for the sample. The main goal of random sampling is to obtain an unbiased representation of the population, which allows for more accurate and generalizable results.

Analyzing the polling technique

In the given scenario, viewers who agree or disagree with the issue can call a specified 900 number to express their opinions. However, this technique is not likely to result in a random sample. Some reasons for this include: 1. Only those viewers who are watching the program will be aware of the poll and have the opportunity to participate. 2. Viewers who have stronger opinions on the issue may be more likely to call and participate, leading to a sample that is not representative of the overall population's opinion. 3. The fact that respondents have to pay a fee for their calls may discourage some people from participating, further skewing the sample.

Discussing the validity of the survey results

Due to the non-random nature of the sample collected using this polling technique, the validity of the survey results may be questionable. This is because the sample likely does not accurately represent the general population's opinions, and thus, the survey results may not be generalizable to the whole population.

Considering the margin of error

The margin of error is an essential aspect to consider in any survey or poll because it quantifies the uncertainty in survey results. However, as the polling technique used in this scenario does not result in a random sample, calculating a margin of error may not provide any meaningful information. It could even be misleading because the primary sources of bias in the survey results stem from the non-random nature of the sample rather than the sample size or other factors typically taken into account when calculating the margin of error. In conclusion, the polling technique in the given scenario does not result in a random sample, and the validity of the survey results may be questionable. Due to the non-random nature of the sample, calculating a margin of error may not be relevant or meaningful in this case.

Key concepts

Validity of Survey Results

When discussing the validity of survey results, what we're essentially questioning is how well the survey reflects the actual opinions or behaviors of the general population. It's crucial for the results to be a true mirror of the population to make informed decisions or to accurately understand the issue at hand.

As highlighted in our exercise, if a survey method introduces biases—as is the case with calling a premium-rate phone number—it challenges the validity of its results. Such biases can arise from self-selection, cost barriers, and a limited audience fragment. For instance, only those passionate about the issue or who can bear the cost are likely to participate, leading to unrepresentative results. This skews the survey outcomes, making it an unreliable source for drawing conclusions about the wider public opinion.

To ensure validity, a survey must aim to reduce biases. This includes but is not limited to demographic representation, accessibility, and the removal of any prohibitive costs or other barriers that might exclude certain groups from the sample. Random sampling serves this purpose because every member of the populace stands an equal chance of selection, minimizing the chance for biases and ensuring that results are as valid as possible.

Margin of Error

The margin of error indicates the level of precision of the results of a survey. It's a statistical way to measure the expected range within which the true value lies, given the sample size and confidence level. Think of it as a buffer zone that accounts for the natural variation in responses if you were to repeat the survey multiple times.

In the exercise, the lack of random sampling makes it inappropriate to calculate a margin of error because its foundation relies on the assumption of a random sample. Without randomness, the margin of error cannot accurately reflect the extent of uncertainty about the survey's results. Furthermore, even if a margin of error was calculated, it would not account for the systematic biases introduced by the methodology of soliciting opinions through a fee-based phone call system, hence presenting a false sense of precision.

To correctly apply the margin of error, one must obtain a sample that's representative of the entire population. This allows pollsters to extrapolate their findings and estimate a range where the true opinion or behavior measurement would fall, should the entire population be surveyed.

Survey Methodology

Diving into the world of survey methodology, the process encompasses the planning, collection, and analysis of data from a group of individuals. This methodology impacts the accuracy and reliability of the survey's conclusions. Effective survey methodology follows a structured approach that includes defining the target population, choosing an appropriate sampling method, designing the survey instrument (like questionnaires or interviews), and ultimately, data collection that minimizes bias.

In our exercise, the methodology of having viewers call in to express their opinions is flawed. First off, it doesn't capture a random sample of the audience, narrowing the breadth of opinions to a particular type of respondent. Additionally, the pay-to-vote aspect introduces economic bias, failing to account for a major section of the audience that may not want or be able to incur the cost.

An improved methodology would involve a strategy that ensures every individual in the population has an equal opportunity to respond, without the barrier of costs. Moreover, employing strategies like stratified sampling or using technology like online surveys could also significantly enhance the inclusivity and accuracy of the survey results, translating to a more reliable overview of the public's stance on any given issue.