Researchers Observed A Random Sample Of Drivers And Recorded Data About Their Phone Usage While Driving. The Researchers Saw 160 Of The 800 Women In The Sample Using Phones, While 300 Of The 1200 Men Were Seen Using Phones.The Researchers Want To Test
Introduction
The use of mobile phones while driving is a significant concern for road safety. Researchers have been studying this issue to understand its prevalence and potential consequences. In this article, we will discuss a statistical analysis of phone usage while driving, based on a random sample of drivers. The researchers observed 800 women and 1200 men, recording data on their phone usage while driving. The results showed that 160 women and 300 men were using their phones while driving. We will use these data to test a hypothesis about phone usage while driving.
Hypothesis
The researchers want to test the following hypothesis:
H1: The proportion of women using phones while driving is less than the proportion of men using phones while driving.
Null Hypothesis
The null hypothesis is:
H0: The proportion of women using phones while driving is equal to the proportion of men using phones while driving.
Data Analysis
To test the hypothesis, we need to calculate the proportions of women and men using phones while driving. We can use the following formulas:
Proportion of women using phones = (Number of women using phones) / (Total number of women) Proportion of men using phones = (Number of men using phones) / (Total number of men)
Using the given data, we can calculate the proportions as follows:
Proportion of women using phones = 160 / 800 = 0.20 Proportion of men using phones = 300 / 1200 = 0.25
Chi-Square Test
To test the hypothesis, we can use the chi-square test. The chi-square test is a statistical test used to determine whether there is a significant association between two categorical variables. In this case, the two categorical variables are "gender" and "phone usage while driving".
The chi-square test statistic is calculated as follows:
χ² = Σ [(observed frequency - expected frequency)² / expected frequency]
where Σ denotes the sum over all categories.
The expected frequency is calculated as follows:
Expected frequency = (Row total × Column total) / Grand total
Using the given data, we can calculate the expected frequencies as follows:
Expected frequency for women using phones = (800 × 300) / 2000 = 120 Expected frequency for women not using phones = (800 × 900) / 2000 = 360 Expected frequency for men using phones = (1200 × 300) / 2000 = 180 Expected frequency for men not using phones = (1200 × 900) / 2000 = 540
The chi-square test statistic is calculated as follows:
χ² = [(160 - 120)² / 120] + [(640 - 680)² / 680] + [(300 - 180)² / 180] + [(900 - 920)² / 920] = 40 + 40 + 400 + 40 = 520
P-Value
The p-value is the probability of observing a chi-square test statistic at least as extreme as the one observed, assuming that the null hypothesis is true. The p-value can be calculated using a chi-square distribution table or a statistical software package.
Using a chi-square distribution table, we can find the p-value as follows:
p-value = P(χ² ≥ 520) = 0.0001
Conclusion
Based on the chi-square test, we can reject the null hypothesis and conclude that the proportion of women using phones while driving is less than the proportion of men using phones while driving. This suggests that men are more likely to use their phones while driving than women.
Limitations
This study has several limitations. Firstly, the sample size is relatively small, which may affect the accuracy of the results. Secondly, the study only includes drivers from a specific region, which may not be representative of drivers from other regions. Finally, the study only measures phone usage while driving and does not account for other factors that may influence phone usage, such as age, education level, and driving experience.
Future Research
Future research should aim to address these limitations by increasing the sample size, including drivers from different regions, and accounting for other factors that may influence phone usage. Additionally, researchers should explore the potential consequences of phone usage while driving, such as accidents and near-misses, to better understand the risks associated with this behavior.
References
- National Highway Traffic Safety Administration. (2020). Traffic Safety Facts: Distracted Driving.
- American Automobile Association. (2020). Distracted Driving: A Growing Concern.
- World Health Organization. (2018). Global Status Report on Road Safety 2018.
Appendix
The following table summarizes the data used in this analysis:
| Gender | Using Phones | Not Using Phones | Total | |
|---|---|---|---|---|
| Women | 160 | 640 | 800 | |
| Men | 300 | 900 | 1200 | |
| Total | 460 | 1540 | 2000 |
Q: What is the main purpose of this study?
A: The main purpose of this study is to investigate the prevalence of phone usage while driving and to test a hypothesis about the difference in phone usage between men and women.
Q: What is the hypothesis being tested?
A: The hypothesis being tested is that the proportion of women using phones while driving is less than the proportion of men using phones while driving.
Q: What is the null hypothesis?
A: The null hypothesis is that the proportion of women using phones while driving is equal to the proportion of men using phones while driving.
Q: How was the data collected?
A: The data was collected by observing a random sample of drivers and recording data on their phone usage while driving.
Q: What are the results of the study?
A: The results of the study show that 160 women and 300 men were using their phones while driving. The chi-square test was used to test the hypothesis, and the results show that the proportion of women using phones while driving is less than the proportion of men using phones while driving.
Q: What is the p-value of the study?
A: The p-value of the study is 0.0001, which indicates that the results are statistically significant.
Q: What are the implications of the study?
A: The study suggests that men are more likely to use their phones while driving than women. This has implications for road safety and public health.
Q: What are the limitations of the study?
A: The study has several limitations, including a relatively small sample size and a lack of representation from different regions.
Q: What are the potential consequences of phone usage while driving?
A: The potential consequences of phone usage while driving include accidents and near-misses.
Q: What are the recommendations for future research?
A: Future research should aim to address the limitations of the study by increasing the sample size, including drivers from different regions, and accounting for other factors that may influence phone usage.
Q: What are the references for this study?
A: The references for this study include the National Highway Traffic Safety Administration, the American Automobile Association, and the World Health Organization.
Q: What is the appendix of the study?
A: The appendix of the study includes a table summarizing the data used in the analysis.
Frequently Asked Questions
- Q: Is phone usage while driving a significant concern for road safety? A: Yes, phone usage while driving is a significant concern for road safety.
- Q: What are the potential consequences of phone usage while driving? A: The potential consequences of phone usage while driving include accidents and near-misses.
- Q: How can phone usage while driving be prevented? A: Phone usage while driving can be prevented by using hands-free devices, putting phones on silent mode, and avoiding distractions while driving.
- Q: What are the implications of the study for public health? A: The study suggests that phone usage while driving is a significant concern for public health, and that men are more likely to use their phones while driving than women.
Conclusion
Phone usage while driving is a significant concern for road safety and public health. The study suggests that men are more likely to use their phones while driving than women, and that phone usage while driving can have serious consequences. Future research should aim to address the limitations of the study and to explore the potential consequences of phone usage while driving.