Suppose that you take a random sample of size n in order to

Suppose that you take a random sample of size n in order to estimate some population proportion, p. Let pn be the sample proportion. (a) Explain what is wrong in the following statements: i. p is unknown, therefore it is a random variable. ii. if n is sufficiently large, an approximate 95% confidence interval for pn, is iii. the sample proportion pn is normally distributed with mean p and variance (b) How much should you increase the sample size in order to cut the standard deviation of pn, sd(pn), in half? (c) What is the largest possible value (as a function of n) that sd(pn) can take? (d) What is the minimum sample size required so that the length of aim approximate 95% confidence internal for p be at most 3% ?

Solution