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2. Consider a population of four values (3, 5, 7, 9). a. Find all possible samples of size 2 which can be drawn without replacement from this population. b. Find the mean of the sampling distribution of means. c. Find the variance of the sampling distribution of the means.

2. Consider a population of four values (3, 5, 7, 9). a. Find all possible samples of size 2 which can be drawn without replacement from this population. b. Find the mean of the sampling distribution of means. c. Find the variance of the sampling distribution of the means.

MATLAB: An Introduction with Applications
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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Let's have another example. Example 2: Consider a population with values (2, 3, 8). Solution: a. Find all possible samples of size 2 which can be drawn without replacement from this population. b. Find the mean of the sampling distribution of means. c. Find the variance of the sampling distribution of means. a. Again, we must make a table with the list of all possible samples. Observation Sample 1 (2, 3) 2 (2,8) 3 (3, 2) 4 (3,8) 5 (8, 2) 6 (8,3) Notice that the observation was lessen because there was not repletion of the values in each sample. b. Add another column for the average/ mean of each sample. Then compute for the mean of the sampling distribution of the mean. Observation Sample X Ex 1 fx (2, 3) 2.5 H₂ = n 2 (2,8) 5 3 (3, 2) 2.5 Hx= 26 6 4 (3,8) 5.5 5 (8, 2) 5 H = 4.33 6 (8,3) 5.5 Σ x = 26 So the mean of the sampling distribution of the mean is 4.33. c. Computing for the variance of the sampling distribution of the means, we have Observation Sample x x-μz (x-μ)² Σ(x-μ.)2 0} 1 (2, 3) 2.5 -1.83 3.3489 n 2 (2,8) 5 0.67 0.4489 3 (3, 2) 2.5 -1.83 3.3489 σ² = 10.3334 6 4 (3, 8) 5.5 1.17 1.3689 5 (8, 2) 5 0.67 0.4489 1.3689 o = 1.7222 6 (8,3) 5.5 1.17 Σ* Σ(x-μ₂)² = So the variance is 1.72. = 26 10.3334 Now it's your turn to practice. Practice Exercise 1. Consider a population of four values (4, 6, 8). a. Find all possible samples of size 2 which can be drawn with replacement from this population. b. Find the mean of the sampling distribution of means. c. Find the variance of the sampling distribution of means. 2. Consider a population of four values (3, 5, 7, 9). a. Find all possible samples of size 2 which can be drawn without replacement from this population. b. Find the mean of the sampling distribution of means. c. Find the variance of the sampling distribution of the means. ง =
Transcribed Image Text:Let's have another example. Example 2: Consider a population with values (2, 3, 8). Solution: a. Find all possible samples of size 2 which can be drawn without replacement from this population. b. Find the mean of the sampling distribution of means. c. Find the variance of the sampling distribution of means. a. Again, we must make a table with the list of all possible samples. Observation Sample 1 (2, 3) 2 (2,8) 3 (3, 2) 4 (3,8) 5 (8, 2) 6 (8,3) Notice that the observation was lessen because there was not repletion of the values in each sample. b. Add another column for the average/ mean of each sample. Then compute for the mean of the sampling distribution of the mean. Observation Sample X Ex 1 fx (2, 3) 2.5 H₂ = n 2 (2,8) 5 3 (3, 2) 2.5 Hx= 26 6 4 (3,8) 5.5 5 (8, 2) 5 H = 4.33 6 (8,3) 5.5 Σ x = 26 So the mean of the sampling distribution of the mean is 4.33. c. Computing for the variance of the sampling distribution of the means, we have Observation Sample x x-μz (x-μ)² Σ(x-μ.)2 0} 1 (2, 3) 2.5 -1.83 3.3489 n 2 (2,8) 5 0.67 0.4489 3 (3, 2) 2.5 -1.83 3.3489 σ² = 10.3334 6 4 (3, 8) 5.5 1.17 1.3689 5 (8, 2) 5 0.67 0.4489 1.3689 o = 1.7222 6 (8,3) 5.5 1.17 Σ* Σ(x-μ₂)² = So the variance is 1.72. = 26 10.3334 Now it's your turn to practice. Practice Exercise 1. Consider a population of four values (4, 6, 8). a. Find all possible samples of size 2 which can be drawn with replacement from this population. b. Find the mean of the sampling distribution of means. c. Find the variance of the sampling distribution of means. 2. Consider a population of four values (3, 5, 7, 9). a. Find all possible samples of size 2 which can be drawn without replacement from this population. b. Find the mean of the sampling distribution of means. c. Find the variance of the sampling distribution of the means. ง =
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