A large university offers STEM (science, technology, engineering, and mathematics) internships to women in STEM majors at the un
iversity. 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.
(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.
(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.
1 answer:
Answer:
It appears that your question does not include the necessary table; here it is:
Answer: a) 0.223 b) 0.0322 c) more likely
Explanation:
A) This represents the probability that a randomly selected woman does not meet the age criterion.
∑ p ( x ≤ 20 ) = p( x = 17 ) + p(x = 18 ) + p(x = 19 )
= 0.005 + 0.107 + 0.111 = 0.223
B) This indicates the probability that at least 30 out of 100 women will not fulfill the requirement.
30% of 100 is 30. The general probability that selected women will not meet the requirement is 0.223, therefore, the probability of at least 30 out of 100 not qualifying will be = 0.0322.
C) In evaluation of a stratified random sampling, we apply the standard error of proportion to the simple random sampling.
In simple random sampling, the probability = 30/100 = 0.3 (for 30 women not meeting the requirement)
The standard error of proportion =
n = number of observations = 100
p = probability of success = 0.3
Thus, the standard error of proportion = 0.0458.
This helps in determining the likelihood of 30 women who do not meet the age requirement in a stratified sampling.
P ( x ≥ 30 ) = P ( z ≥ ( 0.3 - 0.3 )/ standard error of proportion )
= P ( z ≥ (0)/0.0458) which results in P ( Z ≥ 0 ) = 0.5.
In a stratified sampling, a woman not meeting the age criteria is more likely to be selected.
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