Question

If the population is normally distributed, both the sample mean and the median are unbiased estimators of the population mean O А True o B False O с Not sure Unanswered . 1 attempt left Submit Question 4 Homework. Unanswered A sample statistic such that the mean of all its possible values equals the population parameter the statistic seeks to estimate is an unbiased estimator. А True B False

Answer 1

Ans: If population is normally distributed then both sample mean and sample median are unbaised estimator of popuation mean. Because for a normal distribution population is symmetrical; which means that mean = median . An estimator is said to be unbiased if its expected value is aproximately equal to population parameter; Thus expected value of sample mean in case of normally distributed population is eqaul to population mean. Let
X
= sample mean and $\mu }$ = population mean and M = sample median

Then E(
X
) =  $\mu }$ in this case expected value of sample mean = population mean.

and because mean = medain in normal distribution. so E(M) = $\mu }$ where M = sample median

Correct option is A. It is true.

Ans14 It is true. Because for an unbiased estimtor its expected value is aproximately equal to population parameter. Because in the above case sample statistic has mean of its sampling distribution equal to population parameter, so it is an unbiased estimator.

Because mean of sample statistic = population parameter

E(
X
) =  $\mu }$ in this case expected value of sample mean = population mean.

Ans 15 It is true. Because bias is the difference between an estimator's expected value and its true poulation parameter . So bias = E($\hat{\Theta }$) - ${\Theta }$ .

where E($\hat{\Theta }$) = estimator's expected value and ${\Theta }$ = true population parameter.