Consider taking a random sample of size 10 from the populati

Consider taking a random sample of size 10 from the population of students at a certain college and asking each of the 10 students whether or not they smoke. In the context of this setting, explain what is meant by the sampling distribution of the ordinary sample proportion.

Solution

sampling distribution of p-hat is the probability distribution of p-hat. This could be normal if sample size was high (using central limit theorem). Here, the sampling distribution would be equivalent to corresponding binomial distribution with x = n*p-hat