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If a random sample of size two is taken without replacement from a population containing the units a,b,c and d then the possible samples are
- a)(a, b),(a, c),(a, d)
- b)(a, b),(b, c), (c, d)
- c)(a, b), (b, a), (a, c),(c,a), (a, d), (d, a)
- d)(a, b), (a, c), (a, d), (b, c), (b, d), (c,d)
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If a random sample of size two is taken without replacement from a pop...
Explanation:
In this question, we are given a population that contains units a, b, c, and d. We need to find all possible samples of size two that can be taken from this population without replacement.
Step 1: Understanding the concept
To understand the question, we need to first understand the concept of sampling without replacement. When we take a sample without replacement, it means that once we have selected an item from the population, we cannot select it again in subsequent selections.
Step 2: Listing all possible samples
To find all possible samples of size two, we need to consider all combinations of two units from the population. Since the order of selection does not matter (e.g., selecting a and then b is the same as selecting b and then a), we only need to list unique combinations.
The possible samples are as follows:
- (a, b)
- (a, c)
- (a, d)
- (b, c)
- (b, d)
- (c, d)
Step 3: Checking the options
Now that we have listed all possible samples, we can check which option matches our findings.
Option A: (a, b), (a, c), (a, d)
- This option is missing (b, c) and (b, d), so it is incorrect.
Option B: (a, b), (b, c), (c, d)
- This option matches our findings exactly, so it is a possible correct answer.
Option C: (a, b), (b, a), (a, c), (c, a), (a, d), (d, a)
- This option includes repetitions such as (b, a) and (c, a), which are not allowed in sampling without replacement. Therefore, it is incorrect.
Option D: (a, b), (a, c), (a, d), (b, c), (b, d), (c, d)
- This option matches our findings exactly, so it is a possible correct answer.
Conclusion:
Based on the analysis, options B and D both match the possible samples. Therefore, both options B and D can be considered correct answers for this question.
In this question, we are given a population that contains units a, b, c, and d. We need to find all possible samples of size two that can be taken from this population without replacement.
Step 1: Understanding the concept
To understand the question, we need to first understand the concept of sampling without replacement. When we take a sample without replacement, it means that once we have selected an item from the population, we cannot select it again in subsequent selections.
Step 2: Listing all possible samples
To find all possible samples of size two, we need to consider all combinations of two units from the population. Since the order of selection does not matter (e.g., selecting a and then b is the same as selecting b and then a), we only need to list unique combinations.
The possible samples are as follows:
- (a, b)
- (a, c)
- (a, d)
- (b, c)
- (b, d)
- (c, d)
Step 3: Checking the options
Now that we have listed all possible samples, we can check which option matches our findings.
Option A: (a, b), (a, c), (a, d)
- This option is missing (b, c) and (b, d), so it is incorrect.
Option B: (a, b), (b, c), (c, d)
- This option matches our findings exactly, so it is a possible correct answer.
Option C: (a, b), (b, a), (a, c), (c, a), (a, d), (d, a)
- This option includes repetitions such as (b, a) and (c, a), which are not allowed in sampling without replacement. Therefore, it is incorrect.
Option D: (a, b), (a, c), (a, d), (b, c), (b, d), (c, d)
- This option matches our findings exactly, so it is a possible correct answer.
Conclusion:
Based on the analysis, options B and D both match the possible samples. Therefore, both options B and D can be considered correct answers for this question.
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Community Answer
If a random sample of size two is taken without replacement from a pop...
Without replacement- Ncn = 4c2 = 6Option d has 6 (without replacement)(a , b).....
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