Question

1. Suppose in a survey of n = 2000 students, 1200 responded that they prefer small classes and 800 responded that they prefer large classes. Let p denote the fraction of all students who preferred small classes at the time of the survey, and X ̄ be the fraction of survey respondents who preferred small classes. (Hint: X is distributed as a Bernoulli random variable) (a) Show that E(X ̄) = p and Var(X ̄) = p(1 − p)/n. (b) Use the survey result to estimate p, and calculate the standard error of your estimator. (Hint: Notice that this is the same as estimating the sample mean)

Answer 1