Suppose 1000 iPhones are produced at a factory today....

Suppose 1000 iPhones are produced at a factory today. Management would like to ensure that the phones' display screens meet their quality standards before shipping them to retail stores. Since it takes about 10 minutes to inspect an individual phone's display screen, managers decide to inspect a sample of 20 phones from the day's production. (a) Explain why it would be difficult for managers to inspect an SRS of 20 iPhones that are produced today. (b) $\mathrm{An}$ eager employee suggests that it would be easy to inspect the last 20 iPhones that were produced today. Why isn't this a good idea? (c) Another employee recommends a different sampling method: Randomly choose one of the first 50 iPhones produced. Inspect that phone and every fifticth iPhone produced afterward. (This method is known as systematic random sampling.) Explain carefully why this sampling method is not an SRS.

Suppose 1000 iPhones are produced at a factory today. Management would like to ensure that the phones' display screens meet their quality standards before shipping them to retail stores. Since it takes about 10 minutes to inspect an individual phone's display screen, managers decide to inspect a sample of 20 phones from the day's production. (a) Explain why it would be difficult for managers to inspect an SRS of 20 iPhones that are produced today.
(b) $\mathrm{An}$ eager employee suggests that it would be easy to inspect the last 20 iPhones that were produced today. Why isn't this a good idea?
(c) Another employee recommends a different sampling method: Randomly choose one of the first 50 iPhones produced. Inspect that phone and every fifticth iPhone produced afterward. (This method is known as systematic random sampling.) Explain carefully why this sampling method is not an SRS.

Key Concepts

Simple Random Sampling (SRS)

Simple random sampling is a method of selecting a subset of individuals from a larger population where every individual has an equal chance of being chosen. This ensures that the sample is unbiased and representative of the whole population. In the context of production, practical issues such as imprecisely tracking or labeling every item as it's produced can make achieving true randomness challenging, as implementing an SRS might require additional logistical steps that are not always feasible in fast-paced manufacturing environments.

Systematic Random Sampling

Systematic random sampling involves selecting members of a population at fixed, regular intervals after a random starting point. While it can sometimes be easier to carry out than a true simple random sample, it is not equivalent to an SRS because the selection probabilities are influenced by the physical arrangement or production order. If there is a systematic pattern in the production process, this method can introduce bias, potentially leading to a non-representative sample and affecting the quality control process.

Sampling Bias and Representativeness

Sampling bias occurs when certain members of the population are more likely to be included in the sample than others, leading to results that are not representative of the entire population. In quality control, ensuring that the sampled items accurately reflect the overall production is crucial. Choices like selecting the final items in a production run or employing a systematic method without considering production order can inadvertently introduce bias, undermining the objectives of fair quality checks.

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