Final answer:
The question involves calculating a 90 percent confidence interval for estimating the true proportion of a population with a specified characteristic and determining the sample size required for a desired margin of error using confidence interval formulas.
Step-by-step explanation:
The question pertains to estimating the proportion of a population that exhibits a particular characteristic (in this case, being vegetarians) at a specified confidence level. A 90 percent confidence interval is a range within which the true percentage of the population characteristic is expected to fall, given the sample data. Constructing a confidence interval involves several steps, including determining the sample proportion, calculating the margin of error using a z-score that corresponds to the desired confidence level (in this case, z-score for 90%), and finally computing the confidence interval using these values.
To estimate the minimum sample size necessary for a given margin of error, the formula z² p'q' / E² is used, where p' is the sample proportion, q' is 1 - p', z is the z-score for the desired confidence level, and E is the margin of error.