A geotechnical researcher wants to know if adding a specific enzymatic liquid stabilizer to a local clay soil improves its Unconfined Compressive Strength (UCS). They collect 20 identical soil samples. They leave 10 samples untreated (the control) and treat the other 10 with a $5\%$ solution of the enzyme. After a 7-day curing period, they test all 20 samples to failure in a compression machine. What type of research design is this?

A transportation engineer wants to understand the relationship between weather conditions and average highway speeds on Interstate 95. For one year, they collect existing data from road sensors (speed, volume) and local weather stations (rainfall, temperature, visibility). They analyze the data to see if average speeds drop significantly during heavy rain compared to clear days. What type of research design is this?

A study investigates the effect of three different curing methods (water ponding, wet burlap covering, and a sprayed chemical curing compound) on the 28-day splitting tensile strength of a standard $30\text{ MPa}$ concrete mix. Identify the independent, dependent, and at least two control variables.

An urban planner is researching how the width of a crosswalk ($2m$, $4m$, or $6m$) affects the average crossing time of pedestrians during peak rush hour at a specific intersection. Identify the independent and dependent variables.

A city introduces a new Light Rail Transit (LRT) line. To evaluate its success, researchers first analyze ridership data (ticket sales, tap-in/tap-out data) over six months to quantify usage patterns across different demographics and times of day. They then conduct in-depth focus groups with residents from low-ridership neighborhoods to understand why they are not using the LRT. Explain how this is a mixed-methods design and its benefit.

Compare the primary data collection methods a structural engineer might use to assess the fatigue life of a steel bridge girder versus an environmental engineer assessing the water quality of a river downstream from an industrial plant.

A state DOT wants to survey the condition of its 5,000 bridges. They only have the budget to inspect 100 bridges. Approach A: They assign a number (1-5000) to every bridge and use a random number generator to select 100 bridges. Approach B: They divide the 5,000 bridges into three categories based on age (Built before 1970, 1970-2000, post-2000). They then randomly select a proportionate number of bridges from each of these three age categories to reach 100 total. Categorize these sampling techniques and explain why Approach B might be preferred.

Following a series of highly publicized balcony collapses in a coastal city, a forensic engineering team is hired to investigate. There are thousands of balconies in the city. Instead of randomly selecting balconies to inspect, the team specifically chooses to inspect only balconies on buildings built between 1995 and 2005, facing directly toward the ocean, and constructed using a specific type of cantilevered wood framing. What type of sampling is this?

A concrete supplier wants to estimate the mean compressive strength of a batch of 10,000 precast concrete pavers ($N = 10,000$). They want to be 95% confident ($Z = 1.96$) that their sample mean is within $1.5\text{ MPa}$ ($e = 1.5$) of the true population mean. Based on past data, the standard deviation of strength is known to be $4.0\text{ MPa}$ ($\sigma = 4.0$). Calculate the required sample size using Yamane's simplified formula as a starting point, then explain why the more complex formula is actually needed here.

A transportation department wants to conduct a survey to estimate the proportion ($p$) of commuters in a large metropolitan area who would switch to public transit if fares were halved. The total population is unknown but very large (assume infinite). They want a 99% confidence level ($Z = 2.576$) and a margin of error of $\pm 4\%$ ($e = 0.04$). Since they have no prior data on commuter preferences, they must assume maximum variance. Calculate the required sample size.

A university campus has exactly 2,500 registered student vehicles ($N = 2500$). The parking authority wants to estimate the proportion of these vehicles that are electric (EVs). They desire a 95% confidence level ($Z = 1.96$) and a margin of error of $\pm 5\%$ ($e = 0.05$). A preliminary study last year suggested the proportion of EVs was around $10\%$ ($p = 0.10$). Calculate the required sample size using the finite population correction.

A small municipality has exactly $N = 500$ residential streets. The city engineer wants to estimate the proportion of streets that require immediate pothole repair ($p$). They want a 90% confidence level ($Z = 1.645$) and a margin of error of $\pm 5\%$ ($e = 0.05$). Assume maximum variance ($p = 0.5$). Calculate the required sample size using the finite population correction.