Question

{10} 3.1 [from Agresti and Finlay 2009] "The distribution of family size in a particular tribal society is skewed to the right, with E(Y) = 5.2 and sd(Y) = 3.0. These values are unknown to an anthropologist, who takes a sample of families in this society to estimate mean family size." Let y-bar denote the sample mean family size she obtains, for a random sample of 36 families.

a. "Identify the sampling distribution of y-bar. State its mean and standard error and explain what it describes."

b. "Find the probability that her sample mean falls within 0.5 of the population mean."

{10} 3.2 Yi, i=1,...,n are i.i.d. Bernoulli random variables with p=0.45. Let Y¯ denote the sample mean. Use the central limit theorem to compute approximations for the following:

a. Pr(Y¯>0.49) when n=144.

b. Pr(Y¯<0.41) when n=576.

c. How large would n need to be to ensure that Pr(0.43≤Y¯≤0.47)≥0.95? Set this up as an algebraic expression and solve for n.

Answer 1