Question

Consider the following population: (4,7, 10, 13). Note that the population mean is the following. 4+7+10+'13 -8.5 (a) Suppose that a random sample of sine 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): 4,7 4,10 4,13 7.4 7.10 7.13 10,4 10,7 10, 13 13,4 13,7 13, 10 Compute the sample mean for each of the 12 possible samples Sample Sample Mean Sample Sample Mean 14,7 10,4 4,10 10,7 10, 13 2.4 7. 10 13,7 Entrar 7. 13 13.10 Use this information to construct the sampling distribution of Display the sampling distribution as a density histogram.) R D E Sample mean

Answer 1

(a)

Sample		Sample Mean	Sample		Sample Mean
4	7	5.5		10	4	7
4	10	7		10	7	8.5
4	13	8.5		10	13	11.5
7	4	5.5		13	4	8.5
7	10	8.5		13	7	10
7	13	10		13	10	11.5

Column	Sample Mean	Probability
A	5.5	0.166667
B	7	0.166667
C	8.5	0.333333
D	10	0.166667
E	11.5	0.166667

(b)

Column	Sample Mean	Probability
A	4	0.0625
B	5.5	0.125
C	7	0.1875
D	8.5	0.25
E	10	0.1875
F	11.5	0.125
G	13	0.0625

(c) They are both symmetric about the population mean.

One distribution covers larger range.

One distribution is more scattered than another.

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