# Suppose you are interested in the proportion of students

Suppose you are interested in the proportion of students receiving federal aid at the community colleges in the state of Florida. You take a simple random sample of student records (ensuring that all the colleges are represented according to their size). The sample of 350 student records revealed that 192 students received some sort of federal aid.(a) Calculate the 95% confidence interval for the corresponding population proportion, and interpret the result.(b) Calculate the 99% confidence interval for the corresponding population proportion, and interpret the result.(c) If the margin of error is to be reduced to 0.025 (2.5%) while keeping the confidence level of 99%, what should be the sample size? Assume that the sample proportion is as given above.(d) If the margin of error is to be reduced to 0.025 (2.5%) while keeping the confidence level of 99%, what should be the sample size? Now assume that there is no knowledge about the sample proportion.