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Running Red Lights. A survey about driving habits by academic researchers produced a list of 5024 licensed drivers. 28 The investigators chose an SRS of 880 of these drivers to answer questions about their driving habits. a. How would you assign labels to the 5024 drivers? Choose the first 5 drivers in the sample. If you use Table B, start at line 118 . b. One question asked was, "Recalling the last ten traffic lights you drove through, how many of them were red when you entered the intersections?" Of the 880 respondents, 171 admitted that at least one light had been red. A practical problem with this survey is that people may not give truthful answers. What is the likely direction of the bias: Do you think more or fewer than 171 of the 880 respondents really ran a red light? Why?

Step by step solution

01

Assigning Labels

Each driver in the list of 5024 should be assigned a unique number from 0001 to 5024. This can be done by numbering each driver in the order they appear on the list.

02

How to Select the Sample Using a Table

To select an SRS (Simple Random Sample) of 880 drivers, use a random number table (Table B in this case). Begin at line 118 and read four-digit numbers. Select the numbers that fall within the label range from 0001 to 5024, ignoring duplicates and numbers outside this range, until you have selected 880 different numbers.

03

Choosing the First 5 Drivers Using Table B

Starting at line 118 of Table B, identify the first five four-digit numbers that fall within the range of 0001 to 5024. For example, if you see the sequence 1234, 5678, 0523, 0045, and 6789 in Table B, the selected numbers from this range and within valid limits would be 1234, 0523, 0045.

04

Understanding Survey Question and Identifying Bias

The survey question asks drivers to recall if any of the last ten traffic lights they drove through were red upon entry. Of 880 sampled drivers, 171 admitted running a red light. Consider social desirability bias, where respondents may underreport undesirable actions like running a red light.

05

Analyzing Bias Direction

Given the social desirability bias, it is likely there is underreporting. Therefore, the true number of drivers who ran a red light is probably higher than the 171 who admitted to it.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Survey Bias

Survey bias can significantly impact the accuracy of survey results. When a survey is conducted, biases might occur if the answers are not representative of the entire population. This may happen due to non-random sampling or errors in the survey design. In the context of the driver behavior survey, biases could be introduced if the sample of respondents is not truly random or if certain driver groups are overrepresented or underrepresented.

Two common types of biases are:

• Selection Bias: Occurs when the sample is not randomly selected, making the findings unrepresentative of the broader population.
• Response Bias: Arises when participants do not respond truthfully or accurately, possibly skewing the results.

In the driver behavior survey, response bias is especially relevant as participants might not disclose their true behavior at red lights, influenced by factors like fear of judgment.

Random Number Table

A random number table is crucial for ensuring the sample in a survey is unbiased. It provides a way to select respondents randomly, which is essential for the integrity of the survey's findings. To use the table, researchers assign a unique number to each potential survey participant, ensuring every individual has an equal chance of being selected.

In the study about licensed drivers, a table of random numbers was used to select a Simple Random Sample (SRS) from 5024 drivers. Numbers falling within the range of 0001 and 5024 were selected without replacement until the sample size of 880 was reached.

Using this method:

• Ensures diversity and represents the larger population.
• Reduces the risk of selection bias.
• Is straightforward, especially when using large datasets.

This approach is vital for maintaining the accuracy and reliability of survey results.

Driver Behavior Survey

The driver behavior survey aimed to understand how often drivers run red lights by asking them about their recent driving experiences. Specifically, drivers were asked to report how many of the last ten traffic lights they encountered were red as they entered the intersection.

By using an SRS of 880 drivers from a pool of 5024, the survey hoped to gain insights representative of the entire driver population. This method is essential in research to ensure that the findings are systematic and can be generalized.

Challenges in this survey:

• Honesty of Responses: Drivers may not accurately report running red lights due to fear of legal or social repercussions.
• Memory Errors: Recall-based questions can be inaccurate as respondents might forget or misremember events.

Addressing these challenges can help improve survey accuracy and provide more reliable data.

Social Desirability Bias

Social desirability bias is a significant concern in surveys about socially sensitive behavior, like running red lights. This type of bias occurs when survey respondents provide answers they believe are socially acceptable rather than truthful.

This bias is problematic because:

• It leads to underreporting of undesirable behaviors.
• Causes survey results to deviate from the truth, thus skewing findings.
• Reduces the reliability of the collected data, as it does not reflect actual participant behavior.

In the given survey, some drivers might underreport running red lights, fearing judgment or consequences. As a result, the number of drivers who actually ran a red light is likely higher than the reported figure of 171. Strategies to mitigate social desirability bias in surveys include assuring confidentiality and using indirect questioning techniques.