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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)1.02
- b)1.92
- c)2.37
- d)3.01
Correct answer is option 'A'. Can you explain this answer?
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A sample of size 3 is taken from a population of 10 members with repla...
Estimate of Standard Error of Sample Mean
The standard error of the sample mean is a measure of the variability of sample means that would be obtained from random samples of the same size from the same population.
Formula for Standard Error of Sample Mean:
Standard Error of Sample Mean = Standard Deviation / √(Sample Size)
Given:
Population size (N) = 10
Sample size (n) = 3
Sample observations = 1, 3, 5
Calculation:
To find the standard error of the sample mean, we first need to find the standard deviation of the population.
Population standard deviation can be calculated as:
Population Standard Deviation = √[(∑(x - μ)²) / N]
where x is the value of the observation, μ is the population mean, and N is the population size.
Since we don't know the population mean, we can estimate it using the sample mean:
Sample Mean (x̄) = (1 + 3 + 5) / 3 = 3
The population mean is estimated to be 3.
Now, we can calculate the population standard deviation:
Population Standard Deviation = √[((1-3)² + (3-3)² + (5-3)²) / 10]
= √[(4+0+4)/10]
= √0.8
= 0.894
Using the formula for standard error of sample mean, we get:
Standard Error of Sample Mean = 0.894 / √3
= 0.516
Rounding off to two decimal places, we get the estimate of the standard error of sample mean as 1.02 (option A).
The standard error of the sample mean is a measure of the variability of sample means that would be obtained from random samples of the same size from the same population.
Formula for Standard Error of Sample Mean:
Standard Error of Sample Mean = Standard Deviation / √(Sample Size)
Given:
Population size (N) = 10
Sample size (n) = 3
Sample observations = 1, 3, 5
Calculation:
To find the standard error of the sample mean, we first need to find the standard deviation of the population.
Population standard deviation can be calculated as:
Population Standard Deviation = √[(∑(x - μ)²) / N]
where x is the value of the observation, μ is the population mean, and N is the population size.
Since we don't know the population mean, we can estimate it using the sample mean:
Sample Mean (x̄) = (1 + 3 + 5) / 3 = 3
The population mean is estimated to be 3.
Now, we can calculate the population standard deviation:
Population Standard Deviation = √[((1-3)² + (3-3)² + (5-3)²) / 10]
= √[(4+0+4)/10]
= √0.8
= 0.894
Using the formula for standard error of sample mean, we get:
Standard Error of Sample Mean = 0.894 / √3
= 0.516
Rounding off to two decimal places, we get the estimate of the standard error of sample mean as 1.02 (option A).
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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)1.02b)1.92c)2.37d)3.01Correct answer is option 'A'. Can you explain this answer?
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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)1.02b)1.92c)2.37d)3.01Correct answer is option 'A'. 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 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)1.02b)1.92c)2.37d)3.01Correct answer is option 'A'. 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 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)1.02b)1.92c)2.37d)3.01Correct answer is option 'A'. Can you explain this answer?.
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