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A sample of size 3 is taken from a population of 10 members with replacement. If the sample observations are 1,3 and 5, what is the estimate of the standard error of sample mean?
- a)1.96
- b)2.00
- c)2.25
- d)2.28
Correct answer is option 'B'. Can you explain this answer?
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A sample of size 3 is taken from a population of 10 members with repla...
Calculation of Standard Error of Sample Mean
- The formula for standard error of sample mean is:
Standard Error of Sample Mean = (Standard Deviation of Population) / √(Sample Size)
- As the population standard deviation is not given, we need to estimate it using the sample standard deviation.
- The formula for sample standard deviation is:
Sample Standard Deviation = √([Σ(x - x̄)²] / n)
where Σ represents summation, x is the individual observation, x̄ is the sample mean, and n is the sample size.
Calculation of Sample Standard Deviation
- The sample observations are 1, 3, and 5.
- The sample mean is (1 + 3 + 5) / 3 = 3.
- The deviations from the sample mean are: -2, 0, and 2.
- The squared deviations are: 4, 0, and 4.
- The sum of squared deviations is 8.
- The sample variance is 8 / 2 = 4.
- The sample standard deviation is √4 = 2.
Calculation of Standard Error of Sample Mean
- The sample size is 3.
- The estimated population standard deviation is 2.
- The standard error of sample mean = 2 / √3 ≈ 1.1547.
- Rounding off to two decimal places, we get 1.15.
Conclusion
- The estimate of the standard error of sample mean is 1.15, which is closest to option B (2.00).
- The formula for standard error of sample mean is:
Standard Error of Sample Mean = (Standard Deviation of Population) / √(Sample Size)
- As the population standard deviation is not given, we need to estimate it using the sample standard deviation.
- The formula for sample standard deviation is:
Sample Standard Deviation = √([Σ(x - x̄)²] / n)
where Σ represents summation, x is the individual observation, x̄ is the sample mean, and n is the sample size.
Calculation of Sample Standard Deviation
- The sample observations are 1, 3, and 5.
- The sample mean is (1 + 3 + 5) / 3 = 3.
- The deviations from the sample mean are: -2, 0, and 2.
- The squared deviations are: 4, 0, and 4.
- The sum of squared deviations is 8.
- The sample variance is 8 / 2 = 4.
- The sample standard deviation is √4 = 2.
Calculation of Standard Error of Sample Mean
- The sample size is 3.
- The estimated population standard deviation is 2.
- The standard error of sample mean = 2 / √3 ≈ 1.1547.
- Rounding off to two decimal places, we get 1.15.
Conclusion
- The estimate of the standard error of sample mean is 1.15, which is closest to option B (2.00).
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A sample of size 3 is taken from a population of 10 members with repla...
By using formula of standard error any problem then reply me
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A sample of size 3 is taken from a population of 10 members with replacement. If the sample observations are 1,3 and 5, what is the estimate of the standard error of sample mean?a)1.96b)2.00c)2.25d)2.28Correct answer is option 'B'. Can you explain this answer?
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