Table of contents

1. Intro to Stats and Collecting Data1h 14m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 26m
11. Correlation1h 6m
12. Regression1h 50m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 57m

1. Intro to Stats and Collecting Data

Intro to Stats

Statistics

1. Intro to Stats and Collecting Data

Intro to Stats

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2:30 minutes

Problem 1.r.26

Textbook Question

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.

Verified step by step guidance

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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.

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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