Estimating Proportions- A City Planner’s Approach to Urban Development Analysis

A city planner wants to estimate the proportion of residents in a particular city who are satisfied with the current public transportation system. This is a crucial task as it will help the planner make informed decisions about potential improvements and investments in the city’s transportation infrastructure. Accurate estimation of this proportion is essential for ensuring that the city’s transportation system meets the needs and expectations of its residents.

The city planner faces several challenges in estimating this proportion. Firstly, the city is large and diverse, with a population of over one million residents. This makes it difficult to collect data from a representative sample of the population. Secondly, the residents have varying opinions and experiences with the public transportation system, which adds complexity to the estimation process. Lastly, the planner must consider the time and resources required to conduct a comprehensive survey.

To overcome these challenges, the city planner decides to use a stratified random sampling method. This involves dividing the population into smaller, more manageable groups or strata based on certain characteristics, such as age, income, or neighborhood. By doing so, the planner can ensure that the sample is more representative of the entire population.

The first step in the process is to identify the relevant strata. After consulting with local experts and conducting preliminary research, the planner determines that age, income, and neighborhood are the most appropriate criteria. The population is then divided into four strata: young adults (18-25 years old), middle-aged adults (26-45 years old), older adults (46-65 years old), and seniors (65+ years old). Similarly, income levels are categorized as low, middle, and high, while neighborhoods are classified as urban, suburban, and rural.

Next, the planner randomly selects a sample size from each stratum. To ensure that the sample size is proportional to the size of each stratum, the planner uses the following formula:

Sample size = (Stratum size / Total population) Total sample size

This formula helps the planner maintain the representativeness of the sample while also ensuring that the total sample size remains manageable.

Once the sample size is determined for each stratum, the planner proceeds to collect data through a survey. The survey includes questions about residents’ satisfaction with the public transportation system, as well as their demographic information. The survey is distributed to the selected participants, who are then asked to complete it online or by mail.

After collecting the survey responses, the planner analyzes the data to estimate the proportion of satisfied residents. This involves calculating the percentage of respondents who indicate that they are satisfied with the public transportation system. The planner also considers the margin of error and confidence interval to ensure the accuracy of the estimate.

In conclusion, a city planner’s task to estimate the proportion of residents satisfied with the public transportation system is a complex but essential process. By using a stratified random sampling method and carefully analyzing the data, the planner can provide valuable insights for improving the city’s transportation infrastructure. This, in turn, will enhance the quality of life for its residents and contribute to the overall development of the city.