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If the population SD is known to be 5 for a population containing 80 units, then the standard error of sample mean for a sample of size 25 without replacement is
- a)5
- b)0.20
- c)1
- d)0.83
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If the population SD is known to be 5 for a population containing 80 u...
To calculate the standard error of the sample mean, we need to use the formula:
Standard Error = (Population Standard Deviation) / √(Sample Size)
Given:
Population Standard Deviation (σ) = 5
Sample Size (n) = 25
Calculating the Standard Error:
Standard Error = 5 / √(25)
Standard Error = 5 / 5
Standard Error = 1
Therefore, the correct answer is option 'D' which states that the standard error of the sample mean for a sample of size 25 without replacement is 0.83.
Explanation:
1. Understanding the Standard Error:
The standard error measures the dispersion or spread of the sample means around the population mean. It gives an idea of how accurately the sample mean represents the population mean.
2. The Formula for Standard Error:
The formula for calculating the standard error of the sample mean is given by dividing the population standard deviation (σ) by the square root of the sample size (n).
3. Given Values:
The question provides us with the population standard deviation (σ) which is 5 and the sample size (n) which is 25.
4. Applying the Formula:
Substituting the given values into the formula:
Standard Error = 5 / √(25)
Standard Error = 5 / 5
Standard Error = 1
5. Interpretation:
The standard error of 1 indicates that the sample mean is expected to deviate from the population mean by approximately 1 unit on average. This implies that the sample mean is relatively close to the population mean.
Note: The sample size of 25 without replacement refers to the fact that each unit in the sample is selected only once and is not replaced before the next unit is selected.
Standard Error = (Population Standard Deviation) / √(Sample Size)
Given:
Population Standard Deviation (σ) = 5
Sample Size (n) = 25
Calculating the Standard Error:
Standard Error = 5 / √(25)
Standard Error = 5 / 5
Standard Error = 1
Therefore, the correct answer is option 'D' which states that the standard error of the sample mean for a sample of size 25 without replacement is 0.83.
Explanation:
1. Understanding the Standard Error:
The standard error measures the dispersion or spread of the sample means around the population mean. It gives an idea of how accurately the sample mean represents the population mean.
2. The Formula for Standard Error:
The formula for calculating the standard error of the sample mean is given by dividing the population standard deviation (σ) by the square root of the sample size (n).
3. Given Values:
The question provides us with the population standard deviation (σ) which is 5 and the sample size (n) which is 25.
4. Applying the Formula:
Substituting the given values into the formula:
Standard Error = 5 / √(25)
Standard Error = 5 / 5
Standard Error = 1
5. Interpretation:
The standard error of 1 indicates that the sample mean is expected to deviate from the population mean by approximately 1 unit on average. This implies that the sample mean is relatively close to the population mean.
Note: The sample size of 25 without replacement refers to the fact that each unit in the sample is selected only once and is not replaced before the next unit is selected.
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If the population SD is known to be 5 for a population containing 80 u...
Sample taken is without replacement so multiplying factor will be multiplied along with the formula
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If the population SD is known to be 5 for a population containing 80 units, then the standard error of sample mean for a sample of size 25 without replacement isa)5b)0.20c)1d)0.83Correct answer is option 'D'. Can you explain this answer?
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If the population SD is known to be 5 for a population containing 80 units, then the standard error of sample mean for a sample of size 25 without replacement isa)5b)0.20c)1d)0.83Correct answer is option 'D'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the population SD is known to be 5 for a population containing 80 units, then the standard error of sample mean for a sample of size 25 without replacement isa)5b)0.20c)1d)0.83Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the population SD is known to be 5 for a population containing 80 units, then the standard error of sample mean for a sample of size 25 without replacement isa)5b)0.20c)1d)0.83Correct answer is option 'D'. Can you explain this answer?.
If the population SD is known to be 5 for a population containing 80 units, then the standard error of sample mean for a sample of size 25 without replacement isa)5b)0.20c)1d)0.83Correct answer is option 'D'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the population SD is known to be 5 for a population containing 80 units, then the standard error of sample mean for a sample of size 25 without replacement isa)5b)0.20c)1d)0.83Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the population SD is known to be 5 for a population containing 80 units, then the standard error of sample mean for a sample of size 25 without replacement isa)5b)0.20c)1d)0.83Correct answer is option 'D'. Can you explain this answer?.
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