Question

Suppose a stratified random sampling design is used to select a sample of 30 women who do not meet the age requirement and a sample of 70 women who do meet the age requirement. Based on the probability distribution, is a woman who does not meet the age requirement more likely, less likely, or equally likely to be selected with a stratified random sample than with a simple random sample? Justify your answer.

Answer 1

A woman who does not meet age requirement is more likely to be selected with a stratified random sample than with a simple random sample

Step-by-step explanation:

c) In stratified random sampling, % of women who do not meet the age requirement = 30/100 = 0.30

Standard error of proportion, Cp = Vp(1-p)/n = 0.3(1-0.3)/100 = 0.0458

Probability of at least 30 percent of women not meeting age requirement

P(p > 0.30) = P[Z > (0.30 - 0.30)/0.0458] = P[Z > 0] = 0.5

A woman who does not meet age requirement is more likely to be selected with a stratified random sample than with a simple random sample.