Question

9- The dean of the school wants to know the proportion of students in the school who prefer online classes for the next semester. How do you conduct a research to estimate this proportion by sampling (suppose that you can take only one sample of size n which is smaller than the population size N, and also suppose that a %90 percent confidence interval is fine). - You should explain all steps you take including how you make decision about sample size, what question you ask from the sample, the estimator you choose and the reason for that, how you calculate this estimator, and how you build a confidence interval for the parameter based on this estimator

Answer 1

We should take a sample that is randomly selected of a size >=120 so that it's relatively large to make assumptions about the population of size N.

The question asked to the students would be "Do you prefer Online classes to live classes?" Their responses in the form of Yes/No could be recorded and the sample proportion would be number of people who said yes/n

Then 90% CI for the population proportion p would be given as:

+- z0.05*√(1-)/n

Where z0.05= 1.645 (from the standard normal distribution tables)