(c) suppose a stratified random sampling design is used to select a sample of 30 women who do not meet the…

Explanation:

Step1: Calculate probability in simple - random sample

Let's assume there are (N) total women. The probability of selecting a woman who does not meet the age requirement in a simple - random sample is (P_{srs}=\frac{n_{1}}{N}), where (n_{1}) is the number of women who do not meet the age requirement.

Step2: Calculate probability in stratified - random sample

In the stratified - random sample, we are selecting 30 women who do not meet the age requirement out of the subgroup of non - age - meeting women. Let (n_{1}) be the number of women who do not meet the age requirement. The probability of selecting a woman who does not meet the age requirement in the stratified - random sample is (P_{str}=\frac{30}{n_{1}}). Let's assume there are 100 women in total, and 20 women do not meet the age requirement ((n_{1} = 20)) and 80 women meet the age requirement. In a simple - random sample, (P_{srs}=\frac{20}{100}=0.2). In the stratified - random sample, (P_{str}=\frac{30}{20}=1.5) (this is wrong assumption, we should use the concept of proportion). Let the proportion of women who do not meet the age requirement in the population be (p_{1}) and the proportion of women who meet the age requirement be (p_{2}). The sample size (n = 30 + 70=100). If we assume the proportion of non - age - meeting women in the population is (p), and the number of non - age - meeting women in the population is (N_{1}) and total population is (N). In simple random sampling, the probability of selecting a non - age - meeting woman is (p=\frac{N_{1}}{N}). In stratified random sampling, the probability of selecting a non - age - meeting woman is (\frac{30}{N_{1}}) (where (N_{1}) is the number of non - age - meeting women in the population). Let's assume the proportion of women who do not meet the age requirement in the population is (p). The sample size (n = 100). The probability of selecting a non - age - meeting woman in simple random sampling is (p). The probability of selecting a non - age - meeting woman in stratified random sampling: Let the number of non - age - meeting women in the population be (x) and meeting women be (y). The total population is (N=x + y). The probability of selecting a non - age - meeting woman in stratified random sampling is (\frac{30}{x}), and in simple random sampling is (\frac{x}{x + y}). If we assume the proportion of non - age - meeting women in the population is (p), and we know that the sample is composed of 30 non - age - meeting and 70 age - meeting women. The probability of selecting a non - age - meeting woman in simple random sampling (P_{1}) and in stratified random sampling (P_{2}). Let the number of non - age - meeting women be (a) and age - meeting women be (b). The total population (N=a + b). In simple random sampling, (P_{1}=\frac{a}{a + b}). In stratified random sampling, (P_{2}=\frac{30}{a}). We know that the sample size (n = 100) (30 non - age - meeting and 70 age - meeting). If we assume the proportion of non - age - meeting women in the population is (p), and we sample 30 non - age - meeting out of the non - age - meeting subgroup and 70 age - meeting out of the age - meeting subgroup. The probability of selecting a non - age - meeting woman in simple random sampling: Suppose the number of non - age - meeting women is (n_{1}) and total number of women is (N), (P_{srs}=\frac{n_{1}}{N}). The probability of selecting a non - age - meeting woman in stratified random sampling: (P_{str}=\frac{30}{n_{1}}) (where (n_{1}) is the number of non - age - meeting women in the population). Let's assume the proportion of non - age - meeting women in the population is (0.2) (i.e., if there are 100 women, 20 do not meet the age requirement). In simple random sampling, the probability of selecting a non - age - meeting woman is (P_{srs}=0.2). In stratified random sampling, if there are 20 non - age - meeting women ((n_{1}=20)), the probability of selecting a non - age - meeting woman is (P_{str}=\frac{30}{20}=1.5) (not a probability value in the real sense, we should use the correct formula). The correct way: Let the proportion of non - age - meeting women in the population be (p). The sample size (n = 100) (30 non - age - meeting and 70 age - meeting). The probability of selecting a non - age - meeting woman in simple random sampling (P_{srs}) and in stratified random sampling (P_{str}). Let the number of non - age - meeting women be (n_{1}) and total number of women be (N). (P_{srs}=\frac{n_{1}}{N}), (P_{str}=\frac{30}{n_{1}}) (where (n_{1}) is the number of non - age - meeting women in the population). If we assume the proportion of non - age - meeting women in the population is (p), and we know that the sample is designed as 30 non - age - meeting and 70 age - meeting. The probability of selecting a non - age - meeting woman in simple random sampling: Let the number of non - age - meeting women be (x) and total number of women be (N), (P_{srs}=\frac{x}{N}). The probability of selecting a non - age - meeting woman in stratified random sampling: (P_{str}=\frac{30}{x}). Suppose the proportion of non - age - meeting women in the population is (p). The sample size (n = 100). The probability of selecting a non - age - meeting woman in simple random sampling (P_{srs}) and in stratified random sampling (P_{str}). Let the number of non - age - meeting women be (n_{1}) and total number of women be (N). We know that the proportion of non - age - meeting women in the sample from stratified random sampling is (\frac{30}{30 + 70}=0.3). If we assume the proportion of non - age - meeting women in the population is (p), in simple random sampling the probability of selecting a non - age - meeting woman is (p). If (p<0.3), a woman who does not meet the age requirement is more likely to be selected with a stratified random sample. If (p > 0.3), a woman who does not meet the age requirement is less likely to be selected with a stratified random sample. If (p = 0.3), they are equally likely. Let's assume we know that the proportion of women who do not meet the age requirement in the population is (p). The probability of selection in simple random sampling (P_{srs}=p). The probability of selection in stratified random sampling for non - age - meeting women: The sample has 30 non - age - meeting women out of a total sample of 100. The proportion of non - age - meeting women in the sample is (\frac{30}{100}=0.3). If the proportion of non - age - meeting women in the population (p<0.3), a woman who does not meet the age requirement is more likely to be selected with a stratified random sample. If (p>0.3), she is less likely. If (p = 0.3), she is equally likely. Let's assume we have no prior information about the proportion of non - age - meeting women in the population. But we know that in the stratified sample, the proportion of non - age - meeting women in the sample is (\frac{30}{30 + 70}=0.3). If the actual proportion of non - age - meeting women in the population is less than (0.3), then a non - age - meeting woman is more likely to be selected in the stratified random sample. If the actual proportion is greater than (0.3), a non - age - meeting woman is less likely to be selected in the stratified random sample. If the actual proportion is (0.3), a non - age - meeting woman is equally likely to be selected in both samples.

Answer:

If the proportion of women who do not meet the age requirement in the population is less than (0.3), a woman who does not meet the age requirement is more likely to be selected with a stratified random sample. If the proportion is greater than (0.3), she is less likely. If the proportion is (0.3), she is equally likely.