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4. REASON QUANTITATIVELY It is hypothesized that teens aged 16-18 tend to have more traffic violations than the rest of drivers. A random study of 10,000 drivers between the ages of 16 and 18 found that \( 18 \% \) of the drivers received a traffic citation in the last twelve months. a. What is the margin of error? b. Using the sample mean and the margin of error, what can you conclude? Be sure to correctly identify the population. \( \qquad \) \( \qquad \) \( \qquad \) c. A different group of researchers then randomly selected a group of only 100 drivers of all ages and asked the same question. Ten drivers of the 100 indicated that they had received a traffic citation in the last twelve months. What is the margin of error, the sample mean, and what can you conclude? Again, be sure to correctly identify the population. \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) d. Is there anything that can be reasonably concluded to all drivers? What would be the traffic citations of teenaged drivers compared to all drivers? What would needed to make this study better?

Ask by Fowler Franklin. in Myanmar
Mar 15,2025

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a. The margin of error is about 0.75%. b. The sample mean is 18%. We are 95% confident that between 17.25% and 18.75% of all teen drivers aged 16–18 received a traffic citation in the last twelve months. c. The margin of error is approximately 5.88%, and the sample mean is 10%. We are 95% confident that between 4.12% and 15.88% of all drivers received a traffic citation in the last twelve months. d. Teen drivers have a higher rate of traffic citations compared to all drivers. To make the study better, use larger and more representative samples for both groups to reduce uncertainty.

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Bonus Knowledge

To delve into the historical context, it's interesting to note that teen driving laws have evolved significantly over the years. In the 1980s, many states started implementing graduated licensing systems, aimed at reducing the number of traffic violations and accidents among new teen drivers. This shift led to stricter restrictions on nighttime driving and passenger limits, which are designed to mitigate risk during this crucial learning phase. When it comes to real-world applications, understanding traffic citation trends can influence public policy and education initiatives for safer driving. For instance, with evidence showing that teens tend to have higher violation rates, cities can implement targeted programs—like educational campaigns or behind-the-wheel training workshops—that specifically address the issues facing young drivers. Additionally, insurance companies might adjust premiums or offer discounts for young drivers who take part in such programs, emphasizing the practical importance of this research.

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