CA Foundation Exam > CA Foundation Questions > The statistic T is said to be a consistent es...
Start Learning for Free
The statistic T is said to be a consistent estimator of the population parameter Q if
- a)E(T) = Q
- b)V(T) ⇒ o as n → ∞
- c)Both (A) and (B)
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The statistic T is said to be a consistent estimator of the population...
Consistent Estimator Explanation:
To determine whether a statistic T is a consistent estimator of the population parameter Q, we need to consider two main criteria:
Expectation of T:
- The first criteria is that the expected value of the estimator T should be equal to the population parameter Q. This is denoted by E(T) = Q. If the expected value of T converges to the true population parameter as the sample size approaches infinity, then T is said to be consistent.
Variance of T:
- The second criteria is that the variance of the estimator T should approach zero as the sample size grows larger. This is denoted by V(T) ⇒ 0 as n → ∞. A consistent estimator should have a variance that decreases as more data is collected.
Combination of Criteria:
- If both of these criteria are satisfied, then the statistic T is considered to be a consistent estimator of the population parameter Q. This means that as the sample size increases, the estimator T will provide more accurate estimates of the true population parameter.
Therefore, the correct answer is option 'C' which states that both the expectation of T being equal to Q and the variance of T approaching zero as the sample size increases are necessary conditions for T to be a consistent estimator.
To determine whether a statistic T is a consistent estimator of the population parameter Q, we need to consider two main criteria:
Expectation of T:
- The first criteria is that the expected value of the estimator T should be equal to the population parameter Q. This is denoted by E(T) = Q. If the expected value of T converges to the true population parameter as the sample size approaches infinity, then T is said to be consistent.
Variance of T:
- The second criteria is that the variance of the estimator T should approach zero as the sample size grows larger. This is denoted by V(T) ⇒ 0 as n → ∞. A consistent estimator should have a variance that decreases as more data is collected.
Combination of Criteria:
- If both of these criteria are satisfied, then the statistic T is considered to be a consistent estimator of the population parameter Q. This means that as the sample size increases, the estimator T will provide more accurate estimates of the true population parameter.
Therefore, the correct answer is option 'C' which states that both the expectation of T being equal to Q and the variance of T approaching zero as the sample size increases are necessary conditions for T to be a consistent estimator.
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
|
|
Top Courses for CA FoundationView all
The statistic T is said to be a consistent estimator of the population parameter Q ifa)E(T) = Qb)V(T) ⇒ o as n → ∞c)Both (A) and (B)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
Question Description
The statistic T is said to be a consistent estimator of the population parameter Q ifa)E(T) = Qb)V(T) ⇒ o as n → ∞c)Both (A) and (B)d)None of the aboveCorrect answer is option 'C'. 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 The statistic T is said to be a consistent estimator of the population parameter Q ifa)E(T) = Qb)V(T) ⇒ o as n → ∞c)Both (A) and (B)d)None of the aboveCorrect answer is option 'C'. 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 The statistic T is said to be a consistent estimator of the population parameter Q ifa)E(T) = Qb)V(T) ⇒ o as n → ∞c)Both (A) and (B)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
The statistic T is said to be a consistent estimator of the population parameter Q ifa)E(T) = Qb)V(T) ⇒ o as n → ∞c)Both (A) and (B)d)None of the aboveCorrect answer is option 'C'. 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 The statistic T is said to be a consistent estimator of the population parameter Q ifa)E(T) = Qb)V(T) ⇒ o as n → ∞c)Both (A) and (B)d)None of the aboveCorrect answer is option 'C'. 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 The statistic T is said to be a consistent estimator of the population parameter Q ifa)E(T) = Qb)V(T) ⇒ o as n → ∞c)Both (A) and (B)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
Solutions for The statistic T is said to be a consistent estimator of the population parameter Q ifa)E(T) = Qb)V(T) ⇒ o as n → ∞c)Both (A) and (B)d)None of the aboveCorrect answer is option 'C'. 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 The statistic T is said to be a consistent estimator of the population parameter Q ifa)E(T) = Qb)V(T) ⇒ o as n → ∞c)Both (A) and (B)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The statistic T is said to be a consistent estimator of the population parameter Q ifa)E(T) = Qb)V(T) ⇒ o as n → ∞c)Both (A) and (B)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for The statistic T is said to be a consistent estimator of the population parameter Q ifa)E(T) = Qb)V(T) ⇒ o as n → ∞c)Both (A) and (B)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of The statistic T is said to be a consistent estimator of the population parameter Q ifa)E(T) = Qb)V(T) ⇒ o as n → ∞c)Both (A) and (B)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The statistic T is said to be a consistent estimator of the population parameter Q ifa)E(T) = Qb)V(T) ⇒ o as n → ∞c)Both (A) and (B)d)None of the aboveCorrect answer is option 'C'. 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup