Suppose that the finite population being studied has N elements from which a sample of size n is drawn using SRSWOR to estimate the population totalLOOK AT THE IMAGE ATTACHED NYN =YiTo estimate YN, the estimator YN = Ny, will be used.Given that yn is an unbiased estimator of the population mean YN whereп1YNNYn= -ni=1E[y] = YN, E[ In]= YNShow that YNNỹ, is unbiased for YN. That is, show that E[ YN ] = YN

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Show that YN = Nỹn is unbiased for Yy. That is, show that E[ YN]= YN -

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Suppose that the finite population being studied has N elements from which a sample of size n is drawn using SRSWOR to estimate the population total

LOOK AT THE IMAGE ATTACHED

N
YN =
Yi
To estimate YN, the estimator YN = Ny, will be used.
Given that yn is an unbiased estimator of the population mean YN where
п
1
YN
N
Yn
= -
n
i=1
E[y] = YN, E[ In]
= YN
Show that YN
Nỹ, is unbiased for YN. That is, show that E[ YN ] = YN

Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.

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