In this section, we assumed that the sample size was less than 5% of the size of the population. When sampling without replacement from a finite population in which n ˃ 0.05N, the standard deviation of the distribution of p̂ is given by

where N is the size of the population. A survey is conducted at a college having an enrollment of 6502 students. The student council wants to estimate the percentage of students in favor of establishing a student union. In a random sample of 500 students, it was determined that 410 were in favor of establishing a student union.
(a) Obtain the sample proportion, p̂, of students surveyed who favor establishing a student union.
(b) Calculate the standard deviation of the sampling distribution of p̂ using p̂ as an estimate of p.