CA Foundation Exam > CA Foundation Questions > A sample of size 3 is taken from a population...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
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).
Free Test
FREE
| Start Free Test |
Community Answer
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
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
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?
Question Description
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? 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)1.96b)2.00c)2.25d)2.28Correct answer is option 'B'. 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)1.96b)2.00c)2.25d)2.28Correct answer is option 'B'. Can you explain this answer?.
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? 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)1.96b)2.00c)2.25d)2.28Correct answer is option 'B'. 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)1.96b)2.00c)2.25d)2.28Correct answer is option 'B'. Can you explain this answer?.
Solutions 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)1.96b)2.00c)2.25d)2.28Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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)1.96b)2.00c)2.25d)2.28Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup