EXAMPLE:

Developing a Sampling Distribution . Assume there is a population ... - Population size N=4 B C - Random variable, X, is age of individuals - Values of X: 18, 20, 22, 24 (years) ed in Education, Ins Chap 7-13 Developing a Sampling Distribution (continued) Summary Measures for the Population Distribution: EX, P(x) H = N 18+ 20+22+24 .25 = 21 4 E ( X , - H ) = 2.236 18 20 22 X O = 24 N A B C D Uniform Distribution To MyShared Matritice for Busingon and Economics, $0 0 2007 Pearson Education, Inc Chap 7-14Developing a Sampling Distribution (continued) Now consider all possible samples of size n = 2 1 81 20d Observation Obs 18 20 22 24 16 Sample Means 18 18, 18 18,20 18,22 18,24 1st 20 20,18 20,20 20,22 20,24 2nd Observation Obs 18 20 22 24 22 22,18 22,20 22,22 22,24 18 18 19 20 21 24 24,18 24,20 24,22 24,24 20 19 20 21 22 16 possible samples 22 20 21 22 23 (sampling with 24 23 replacement) 21 22 24 DU MyShared Sentimien for Business and Economics, do 0 2007 Person Education, Inc. Chap 7-15 Developing a Sampling Distribution (continued) Sampling Distribution of All Sample Means 16 Sample Means Sample Means Distribution 1st 2nd Observation Obs 18 20 22 24 P(X) .3 18 18 19 20 21 20 19 20 21 22 22 20 21 22 23 O 24 21 22 23 24 18 19 20 21 22 23 I MyShared 24 X (no longer uniform) Chan 716Developing a Sampling Distribution (continued) Summary Measures of this Sampling Distribution: E(X) - 2X 18+19+21+...+24 N = 21 = H 16 S(XI- H) = N (18-21) +(19-21)+. ..+(24-21) =1.58 16 MyShared Go 7-1 Comparing the Population with its Sampling Distribution Population Sample Means Distribution N = 4 n = 2 H = 21 O = 2.236 Hy = 21 * =1.58 P(X) P(X) 3 .3 .2 .2 -1 0 18 20 22 24 X 18 19 20 21 22 23 24 X A B C D MyShared