Ask Question
25 March, 13:44

If the expected value of the sample statistic is equal to the population parameter being estimated, the sample statistic is said to a. have low variability. b. be an unbiased estimator of the population parameter. c. have high precision. d. be a random estimator of the population parameter.

+5
Answers (1)
  1. 25 March, 13:55
    0
    b. be an unbiased estimator of the population parameter

    Step-by-step explanation:

    The definition of unbiased estimator states that if the population parameter which is to be estimated is equal to the expected value of sample statistic then the estimator will be an unbiased estimator.

    For example consider the sample statistic x bar and population parameter μ the xbar is an unbiased estimator of μ i. e. E (xbar) = μ

    We can show that E (xbar) = μ in the following steps

    Now expected value of sample statistic = E (xbar)

    As we know that xbar = sumxi/n where i ranges from 1 to n. So,

    E (Xbar) = E (sumxi/n)

    n is constant so,

    E (Xbar) = (1/n) E (sumxi)

    where sumxi = x1+x2 + ... + xn.

    E (xbar) = (1/n) (E (x1) + E (x2) + ... + E (xn))

    E (xbar) = (1/n) (μ+μ + ... + μ)

    E (xbar) = (1/n) (nμ)

    E (xbar) = μ

    Hence xbar is an unbiased estimator of population parameter μ.

    So, if the expected value of the sample statistic is equal to the population parameter being estimated, the sample statistic is said to be an unbiased estimator of the population parameter
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “If the expected value of the sample statistic is equal to the population parameter being estimated, the sample statistic is said to a. have ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers