Analyzing Heavy Freight Traffic Data to Support Infrastructure Improvement Decisions

Introduction

The Department of Highway Improvements is tasked with the critical responsibility of repairing a 25-mile stretch of interstate highway. In this endeavor, one of the pivotal considerations is designing a structurally efficient surface capable of withstanding heavy freight traffic. While the average number of heavy-duty trailers on the entire interstate is reported as 72 per hour, the department suspects that the volume of heavy freight traffic on the specific section in question, located within an urban area, may be higher. To validate this theory, the department conducted a comprehensive data collection effort, monitoring the highway for 50 randomly selected 1-hour periods throughout the month. The sample mean and standard deviation were found to be 72 and 13.3, respectively. This essay delves into the statistical analysis of this data and assesses whether it supports the department’s theory.

Hypothesis Testing

The department’s theory implies that the heavy freight traffic on the specific urban section of the highway exceeds the reported average of 72 heavy-duty trailers per hour for the entire interstate. To evaluate this theory statistically, we employ hypothesis testing with a significance level (α) of 0.10.

The null hypothesis (H0) states that the true population mean of heavy-duty trailers on the urban section is equal to the reported average of 72 per hour, while the alternative hypothesis (H1) suggests that it is greater than 72 per hour.

H0: μ = 72 H1: μ > 72

Data Analysis

The sample mean (x̄) is 72, and the sample standard deviation (s) is 13.3. To perform the hypothesis test, we can calculate the test statistic using the formula for a z-test:

�=(�ˉ−�)(�/√�)Z=(s/√n)(xˉ−μ)​

Where:

• �ˉxˉ is the sample mean (72)
• μ is the population mean (72)
• s is the sample standard deviation (13.3)
• n is the sample size (50)

Substituting these values into the formula, we get:

�=(72−72)(13.3/√50)Z=(13.3/√50)(72−72)​ $Z=0$

Now, we can determine the critical value from the z-table for a one-tailed test with α = 0.10. At α = 0.10, the critical z-value is approximately 1.28.

Conclusion

Comparing the calculated test statistic (Z = 0) to the critical value (1.28), we find that Z is less than the critical value. Therefore, we fail to reject the null hypothesis.

In simpler terms, the data does not provide enough evidence to support the theory that the heavy freight traffic on the specific urban section of the highway is greater than the reported average of 72 heavy-duty trailers per hour. The department’s suspicion remains unconfirmed at the 0.10 significance level.

It’s important to note that while this analysis does not support the theory, other factors may need to be considered when making decisions about highway improvements, such as the condition of the road surface, traffic patterns, and safety concerns. Additional data and analyses may be necessary to inform the department’s final decision regarding the structural efficiency of the highway surface in question.