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Ch. 1 - Introduction to Statistics
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 1 - Introduction to StatisticsProblema 1.r.26
Capitolo 1, Problema 1.r.26

Identify the sampling technique used, and discuss potential sources of bias (if any). Explain.
Law enforcement officials stop and check the driver of every third vehicle for blood alcohol content.

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Identify the sampling technique: This is an example of systematic sampling, where a rule is applied to select every third vehicle in a sequence. Systematic sampling involves selecting elements from an ordered population at regular intervals.
Explain the systematic sampling process: In this case, the population is all vehicles passing through a checkpoint, and the sampling interval is every third vehicle. This ensures a structured and predictable selection process.
Discuss potential sources of bias: Systematic sampling can introduce bias if there is a hidden pattern in the population that aligns with the sampling interval. For example, if every third vehicle tends to belong to a specific group (e.g., commercial vehicles or vehicles from a specific area), the sample may not be representative of the entire population.
Consider the randomness of the sample: While systematic sampling is not purely random, it can approximate randomness if the population is evenly distributed and lacks patterns. However, if the traffic flow has periodic patterns, the sample may not be representative.
Conclude with recommendations: To minimize potential bias, law enforcement officials could combine systematic sampling with random starting points or use a different sampling technique, such as simple random sampling, to ensure a more representative sample of drivers.

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Sampling Technique

The sampling technique refers to the method used to select individuals or items from a larger population for analysis. In this case, the technique is systematic sampling, where every third vehicle is chosen for testing. This method can help ensure a more organized and unbiased selection process compared to random sampling, but it may still introduce biases if the pattern of vehicle flow is not random.
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Sampling Distribution of Sample Proportion

Bias in Sampling

Bias in sampling occurs when certain members of a population are systematically more likely to be selected than others, leading to an unrepresentative sample. In the context of the question, potential sources of bias could arise if the traffic patterns or times of day influence which vehicles are stopped, possibly overlooking certain demographics or types of drivers, thus skewing the results.
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Sampling Distribution of Sample Proportion

Systematic Sampling

Systematic sampling is a statistical method where samples are selected from a larger population at regular intervals. This technique is straightforward and can be efficient, but it assumes that the population is ordered in a way that does not introduce bias. In the scenario provided, stopping every third vehicle may inadvertently favor certain types of vehicles or drivers, depending on traffic conditions.
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Sampling Distribution of Sample Proportion
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