For a poll of voters regarding a referendum calling for a national value-added tax, design a sampling method to obtain the inviduals in the sample. Be sure to support your choice. Which sampling method would most likely be used in a poll of voters regarding a referendum calling for a national value-added tax? A. Use simple random sampling. Simple random sampling is always the best sampling method to choose regardless of the survey conducted. B. Use cluster sampling. Each geographical region can be treated as a mini-population because voting results are independent of region. C. Use systematic random sampling. By varying the k-value, a sampling of the whole nation can be selected to achieve the needed accuracy. D. Use convenience sampling. A large number of voters is needed to accurately reflect the nation's voters; so a quick way to collect information is needed. E. Use stratified random sampling. Since this is a national issue, different geographical locations are likely to have similar views.

To determine the most appropriate sampling method for a poll of voters regarding a referendum calling for a national value-added tax, let's analyze each option provided: ### A. Simple Random Sampling - **Description**: Every individual in the population has an equal chance of being selected. - **Pros**: Reduces bias and is straightforward. - **Cons**: May not adequately represent diverse geographical or demographic groups, especially in a national context. ### B. Cluster Sampling - **Description**: The population is divided into clusters (e.g., geographical regions), and entire clusters are randomly selected. - **Pros**: Efficient for large populations and can capture regional differences. - **Cons**: If clusters are not representative of the entire population, it may introduce bias. ### C. Systematic Random Sampling - **Description**: A starting point is randomly selected, and then every k-th individual is chosen. - **Pros**: Simple to implement and can be effective if the population is ordered randomly. - **Cons**: If there is a pattern in the population, it may lead to bias. ### D. Convenience Sampling - **Description**: Individuals are selected based on ease of access. - **Pros**: Quick and easy to gather data. - **Cons**: Highly biased and not representative of the entire population, leading to unreliable results. ### E. Stratified Random Sampling - **Description**: The population is divided into strata (e.g., based on demographics or geography), and random samples are taken from each stratum. - **Pros**: Ensures representation from all segments of the population, which is crucial for a national issue. - **Cons**: More complex to implement than simple random sampling. ### Conclusion Given the nature of the referendum, which is a national issue likely to have varying opinions based on geographical and demographic factors, **E. Use stratified random sampling** is the most appropriate choice. This method ensures that different segments of the population are represented, allowing for a more accurate reflection of the views of the entire nation regarding the value-added tax. Stratified random sampling would allow researchers to capture the diversity of opinions across different regions and demographics, which is essential for understanding the overall sentiment towards the referendum.