Final answer:
The question involves constructing a 90% confidence interval for the proportion of homeless persons who are veterans, with the survey result of a sample of 280 homeless persons where 63 are veterans. The given interval (0.184, 0.266) indicates that there is a 90% confidence that the true population proportion lies within this range.
Step-by-step explanation:
The student's question is about constructing a 90% confidence interval for the proportion of homeless persons who are veterans based on a survey result. To define a confidence interval for a population proportion based on a sample statistic (in this case, the proportion of homeless veterans), statisticians use a formula that incorporates the sample proportion, the sample size, and the desired level of confidence to calculate the margin of error. Then they add and subtract this margin of error from the sample proportion to create a range (the confidence interval) within which they are 90% confident the true population proportion lies.
In the example given, the 90% confidence interval for the proportion of homeless persons who are veterans is (0.184, 0.266). This means that based on the survey data of 280 homeless persons with 63 reporting as veterans, we can be 90% confident that the true proportion of all homeless persons who are veterans is between 18.4% and 26.6%.