Consider the following population: (6, 7, 8, 9). For this population the mean is U=6+7+8+9 4 Suppose that a random sample of size 2 is to be selected without replacement from this population. There are 12 possible samples (provided that the order in which observations are selected 6,7 6,8 6,9 7,6 7,8 7,9 8,6 8,7 8,9 9,6 9,7 9,8 (a) Calculate the sample mean for each of the 12 possible samples. Sample Sample Mean 6,7 6,8 6,9 7,6 7,8 7,9 8,6 8,7 8,9 9,6 = 7.5 9,7 9,8 taken into account).
Consider the following population: (6, 7, 8, 9). For this population the mean is U=6+7+8+9 4 Suppose that a random sample of size 2 is to be selected without replacement from this population. There are 12 possible samples (provided that the order in which observations are selected 6,7 6,8 6,9 7,6 7,8 7,9 8,6 8,7 8,9 9,6 9,7 9,8 (a) Calculate the sample mean for each of the 12 possible samples. Sample Sample Mean 6,7 6,8 6,9 7,6 7,8 7,9 8,6 8,7 8,9 9,6 = 7.5 9,7 9,8 taken into account).
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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Transcribed Image Text:(b) Use the sample means to construct the sampling distribution of x. Display the sampling distribution as a density histogram.
Density
0.8
Density
0.6
0.4
0.2
0.0
0.6
0.4
0.2
6.5
0.0
6
7
6.5
7.5
Sample
Mean
8
7 7.5
Sample
Mean
8 8.5
8.5
9 9.5
Density
DO
0.8
Density
0.6
0.4
0.2
0.0
0.6
0.4
0.2
6.5
0.0
7
6 6.5
7.5
Sample
Mean
8
8.5
7 7.5 8 8.5 9
Sample
Mean
9.5
Density
(c) Suppose that a random sample of size 2 is to be selected, but this time sampling will be done with replacement. Using a method similar to that of part (a), construct the sampling distribution of X. (Hint: There are 16 different possible samples in this case.)
0.8
0.8
0.8
0.8
o
0.8
Density
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
6.5 7
(d) In what ways are the two sampling distributions of parts (b) and (c) similar? In what ways are they different? (Select all that apply.)
Their means are equal.
One distribution is not symmetrical.
They are both symmetrical.
Their means are different.
They both cover the same range.
One distribution covers a larger range.
6
7.5
Sample
Mean
6.5
8
8.5
7 7.5 8 8.5 9
Sample
Mean
9.5
Density
DO
0.8
Density
0.6
0.4
0.2
0.0
0.6
0.4
0.2
6.5
0.0
6
7
6.5
7.5 8
Sample
Mean
8.5
7 7.5 8 8.5 9
Sample
Mean
9.5
Ⓡ
Transcribed Image Text:Consider the following population: {6, 7, 8, 9). For this population the mean is
6 + 7 + 8 + 9
4
μ =
Suppose that a random sample of size 2 is to be selected without replacement from this population. There are 12 possible samples (provided that the order in which observations are selected is taken into account).
8,6
6,7
6,7
6,8
(a) Calculate the sample mean for each of the 12 possible samples.
Sample Sample Mean
6,9
7,6
7,8
7,9
8,6
8,7
8,9
= 7.5
9,6
9,7
6,8 6,9 7,6
9,8
7,8 7,9
8,7 8,9 9,6 9,7 9,8
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