Answer:
The most appropriate interval for the manager to use is:
A) One-sample z-interval for a sample proportion
Here's why:
One-sample: We're dealing with a single population (city residents) and estimating a proportion (percentage favoring the dog park).
z-interval: We're assuming a normal distribution (reasonable for proportions from large populations) and using the sample standard deviation (represented by the z-statistic) to construct the confidence interval.
Sample proportion: We're interested in estimating the proportion of the entire population (city residents) who favor the dog park, based on a sample we'll collect.
The other options are not as suitable:
Population proportion: We don't have data for the entire population, so directly estimating the population proportion isn't feasible.
Difference between proportions: This is used for comparing proportions from two different populations, not a single population.
Two-sample: Similar to the previous point, two-sample methods are for comparing samples from two distinct populations.
