Belk has a chain of department stores across the South. Top management requires that each store manager collect, maintain, and respond to customer complaints (emails, letters, calls, etc.). Each store manager is supposed to keep a list of complaints that have been received. Top management is considering establishing a more formalized method of monitoring and evaluating the responses managers give to the complaints. They want some information that will tell them whether they need to develop such a formalized program or whether they can leave well enough alone and allow managers to use their discretion in handling the complaints. They want to review a sample of these complaints and the responses to them.
a. What sampling plan should be used?
b. Why?
The Correct Answer and Explanation is :
a. Sampling Plan:
The appropriate sampling plan for Belk in this scenario would be stratified random sampling. This method involves dividing the population of customer complaints into distinct groups (or strata) based on certain characteristics, such as type of complaint (product, service, pricing, etc.), store location, or the severity of the complaint. Then, random samples are drawn from each group, and the responses from the store managers are reviewed.
b. Explanation:
A stratified random sampling plan is particularly beneficial in this case because it ensures that various types of customer complaints are well-represented in the sample. Belk’s top management is interested in evaluating whether the managers are handling complaints appropriately and efficiently across different complaint categories. Simply using a random sample might not guarantee a balanced representation of all types of complaints, potentially overlooking specific areas of concern.
In this case, stratification allows for the division of complaints into homogenous subgroups (strata), making the sample more representative of the population as a whole. This is important because complaints in certain areas (such as product issues) may require more attention and different handling strategies compared to complaints about customer service or pricing. By using stratified sampling, managers can ensure that responses to each type of complaint are reviewed, providing a more accurate and detailed understanding of the effectiveness of the current process.
Additionally, by focusing on the different types of complaints or store locations, Belk can identify trends and patterns that might not be visible in a simple random sample. For instance, if a particular store or region is receiving more complaints or handling them less effectively, it would be beneficial for top management to investigate those cases more thoroughly.
Stratified sampling also helps in improving the precision of the estimates by reducing the variability within each stratum. This method ensures that each subgroup is properly represented and that the results of the sampling are more accurate, ultimately helping Belk’s management make more informed decisions about whether a formalized program is necessary or whether managers can continue to handle complaints on their own.
I’ll generate an image to illustrate the stratified random sampling process.
Here’s an illustration showing how stratified random sampling works. It visually represents how customer complaints can be divided into different categories (strata), and random samples are drawn from each group to create a diverse and representative sample. This method ensures all complaint types are well-represented for a thorough evaluation.
