Suppose for a sample of size two to be “representative” of the population, it has to have exactly one man and one woman, and one Democrat and one Republican. What is the chance of selecting a simple random sample of size two from this population that is representative (in this sense of the word)?Group of answer choices1 in 62 in 64 in 101 in 2
Question
Suppose for a sample of size two to be “representative” of the population, it has to have exactly one man and one woman, and one Democrat and one Republican. What is the chance of selecting a simple random sample of size two from this population that is representative (in this sense of the word)?Group of answer choices1 in 62 in 64 in 101 in 2
Solution
To answer this question, we need to make some assumptions since the question does not provide specific information about the population distribution.
Assumption 1: The population is evenly distributed, meaning there are equal numbers of men and women, and equal numbers of Democrats and Republicans.
Assumption 2: The political affiliation is independent of the gender, meaning the probability of being a man or woman does not affect the probability of being a Democrat or Republican, and vice versa.
Given these assumptions, the probability of selecting a man or a woman is 1/2, and the probability of selecting a Democrat or a Republican is also 1/2.
Since we are selecting two people, and they need to be different in both gender and political affiliation, we have four possible combinations: a male Democrat and a female Republican, a male Republican and a female Democrat, a female Democrat and a male Republican, or a female Republican and a male Democrat.
The probability of each combination is (1/2) * (1/2) * (1/2) * (1/2) = 1/16.
Since there are four possible combinations, the total probability is 4 * (1/16) = 1/4.
So, the chance of selecting a simple random sample of size two from this population that is representative (in this sense of the word) is 1 in 4.
Similar Questions
For a simple random sample of size two, all samples of size two have the same chance of being chosen. What would the likelihood be of choosing any one of these samples?Group of answer choices4 in 101 in 62 in 61 in 2
Careful CountingThe audio segment above ends with Charlie McDonnell (of the British “Fun Science” videos) noting that “every now and then, at random, you end up with something awesome.” We might take that to mean that every now and then, a simple random sample is representative of a population with respect to a certain list of demographics. Let’s look at a simple example to see how likely that might be. Suppose you have a population with two men—one a Republican and one a Democrat; and two women—one a Republican and one a Democrat.There are six possible distinct samples of size two from this four-person population. If M = male, F = female, R = Republican, and D = Democrat, then the possible samples are:Group of answer choices(MR, MD), (MR, FR), (MR, FD), (MD,FR), (MD, FD), (FR,FD)(MR, MD), (MR, FR), (MR, FR), (MR,FR), (MD, FD), (FD,FD)(MD, MD), (MD, FR), (MR, FR), (MD,FR), (MD, FD), (FD,FD)(MR, MR), (MR, FD), (MR, FD), (MR,FR), (MD, FD), (FD,FD)
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