Question

(a).A population consists of six numbers 4,8,12,16,20,24.Consider all sample of size two which can be drawn without replacement from this population. Find the following:

The population mean

The population Standard deviation

The mean of sampling distribution of means

The standard deviation of the sample distribution of mean​

Answer 1

Answer:

THE MEAN OF SAMPLEING DISTRIBUTION OF MEANS

HOPE THIS HELPS U

Answer 2

The given question is A population consists of five numbers 3,4,7,8,11Consider all sample of size two which can be drawn without replacement from s

Mean:

$\frac{3 + 4 + 7 + 8 + 11}{5} = \frac{33}{5} = 6.6$

Variance:

$\frac{(( {2 - 6)}^{2} + ( {3 - 6)}^{2} + ( {6 - 6)}^{2} + ( {8 - 6)}^{2} + ( {11 - 6)}^{2} }{5} \\ = 10.8$

Standard deviation=√variance =√10.8=3.286333

The mean of sampling distribution of means:

sampling mean variance

distribution

[2, 2] 2 0

[2, 3] 2.5 0.25

[2, 6] 4 4

[2, 8] 5 9

[2, 11] 6.5 20.25

[3, 3] 3 0

[3, 6] 4.5 2.25

[3, 8] 5.5 6.25

[3, 11] 7 16

[6, 6] 6 0

[6, 8] 7 1

[6, 11] 8.5 6.25

[8, 8] 8 0

[8, 11] 9.5 2.25

[11, 11] 11 0

total 90 67.5

mean of sampling distribution

$\frac{9 0}{15} = 6$

variance

$\frac{67.5}{15} = 4.5$

standard deviation is √variance = √4.5 =2.12

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