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When designing a direct marketing campaign for an online clothing retailer with the aim of quantifying expected response rates by ethnic group, it's crucial to consider the appropriateness of different sampling plans. One of the primary considerations is whether to use a simple random sample or explore alternative sampling methods. Using a simple random sample (SRS) as the sampling plan for testing a direct marketing campaign's response rates by ethnic group has both advantages and disadvantages that need to be assessed in the context of this specific campaign. One significant advantage of SRS is its simplicity and ease of implementation. With SRS, each household in the population has an equal chance of being selected, and this randomness can help minimize selection bias. It's a straightforward method that doesn't require prior knowledge about the population's characteristics, making it suitable for situations where the population is well-defined and can be enumerated accurately. However, when it comes to this particular campaign, the appropriateness of using a simple random sample needs to be critically evaluated. One of the campaign's key objectives is to ensure that the sample accurately reflects the ethnic diversity of the entire US population. This means that the sample should consist of proportions of different ethnic groups that mirror their prevalence in the population. For instance, if Hispanics constitute about 12 percent of the US population, then ideally, 12 percent of the sample should be Hispanic. The problem with using a simple random sample in this context is that it does not guarantee the desired proportionality of ethnic groups in the sample. Randomness can lead to variations where one ethnicity might be overrepresented, and another might be underrepresented. This variability can result in an unrepresentative sample, which can, in turn, lead to inaccurate predictions about response rates among different ethnic groups (Rahman et al., 2022). Stratified sampling, on the other hand, is a more appropriate approach. In stratified sampling, the population is divided into subgroups or strata based on specific characteristics, such as ethnicity. Then, random samples are drawn from each stratum. This method ensures that each ethnic group is proportionally represented in the sample (Bhardwaj, 2019). If Hispanics constitute 12 percent of the US population, 12 percent of the sample will be Hispanic, and the same principle applies to other ethnicities. This approach provides a more accurate representation of the ethnic diversity within the US population and allows for more reliable response rate predictions. Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters to be part of the sample. While this method can be efficient in certain situations, it may not be the best choice here. Cluster sampling could introduce bias if clusters happen to have a significantly higher or lower proportion of a particular ethnicity. Since the goal is to accurately represent ethnic diversity, stratified sampling is preferable. Systematic sampling, where every nth household is selected from a list of the population, also falls short in this context. While it can be efficient, it doesn't guarantee proportionality among ethnic groups. The starting point for systematic sampling is randomly chosen, and if, by chance, it falls within a region or group with an unusual ethnic composition, the sample may not accurately reflect the desired diversity. The choice of sampling plan is crucial when designing a direct marketing campaign to assess response rates by ethnic group. While a simple random sample is straightforward, it may not meet the campaign's goal of mirroring the US population's ethnic diversity within the sample. Stratified sampling is a more appropriate method as it ensures proportional representation of ethnic groups, reducing the risk of bias and providing reliable insights for the marketing campaign. Other methods like cluster or systematic sampling may not align with the campaign's objectives, and careful consideration of the sampling plan is essential to obtain meaningful and actionable results.