Suppose 5000 Sales Invoices Are Separated Into Four Sections

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Suppose that 5,000 sales invoices are separated into four strata. Stratum 1 contains 50 invoices, stratum 2 contains 500 invoices, stratum 3 contains 1,000 invoices, and stratum 4 contains 3,450 invoices. A sample of 500 sales invoices is needed.

a) What type of sampling should you do? Why?

b) Explain how you would carry out the sampling according to the method stated in (a)

c) Why is the sampling in (a) not simple random sampling?

Paper For Above instruction

The problem presented involves selecting a representative sample from a structured population divided into different strata—groups within the population that are distinct but relevant for the sampling purpose. The selection process that best suits such a scenario is stratified sampling. Stratified sampling involves dividing the entire population into mutually exclusive and collectively exhaustive subgroups or strata, then randomly sampling from each subgroup proportionally or equally depending on the research design.

In this specific case, stratified sampling is appropriate because the population of 5,000 sales invoices is already organized into four strata with differing sizes. Because each stratum may have different characteristics or importance, stratified sampling ensures that these differences are properly represented in the sample. By sampling proportionally from each stratum—such as selecting 1% of invoices from each stratum—researchers can achieve a more accurate and precise estimate of the entire population, especially if variable estimates differ across strata.

To carry out stratified sampling, I would first determine the number of invoices to be sampled from each stratum proportionally to their size. For example, stratum 1 contains 50 invoices out of 5,000, which is 1%; hence, it should contribute approximately 1% of the total sample, meaning about 5 invoices. Similarly, stratum 2 comprises 10%, or 50 invoices, which would contribute around 50 samples; stratum 3, with 20%, corresponding to 100 invoices, would contribute perhaps 100 samples; and stratum 4, containing 69%, or 3,450 invoices, would contribute 345 samples. Once the numbers are allocated, simple random sampling techniques can be used within each stratum—such as random number generation—to select the specific invoices. This ensures each invoice within a stratum has an equal chance of selection, preserving randomness while maintaining proportional representation.

This approach differs significantly from simple random sampling of the entire population. In simple random sampling, every invoice from the entire 5,000 would have an equal chance of being selected without regard to the strata, potentially leading to over- or under-representation of certain groups. It could, for instance, result in selecting too many invoices from the smaller strata or neglecting the larger ones, thereby skewing the sample’s representativeness. Stratified sampling thus provides more control and ensures that all segments of the population are adequately represented in the sample, which improves the accuracy of population estimates and the efficiency of the sampling process.

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