Question

C please

A large university offers STEM (science, technology,engineering. and mathematics) internships to women in STEM majors at the university. A woman must be 20 years or older to meet the age requirement for the internships. The table shows the probability distribution of the ages of the women in STEM majors at the university 

Age (years) 17 Probabi 18 20 23 or older 0.063 0,0050.107 0. 0.252 0.249 0.213 

(a) Suppose one woman is selected at random from the women in STEM majors at the university. What is the probability that the woman selected will not meet the age requirement for the internships? 

The university will select a sample of 100 women in STEM majors to participate in a focus group about the internships. 

(b) Suppose a simple random sampling process is used to select the sample of 100 women. What is the probability that at least 30 percent of the women in the sample will not meet the age requirement for the internships?

(c) 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

(c)

In the simple random sample, probability that at least 30 percent of women in the sample will not meet the age requirement is 0.0322.

In stratified random sampling, proportion of women who does not meet the age requirement is $\mu_p$ = 30/100 = 0.30

Standard error of proportion, = 0.0458

Cp = V'p(1-p)/n = V0.3(1-0.3)/100

Probability that at least 30 percent of women in the sample will not meet the age requirement is

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

Thus, the probability that at least 30 percent of women in the sample will not meet the age requirement is higher for stratified random sampling.

So, 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.