Question

A population consists of 5 numbers: 1, 2, 2, 2, 3. Consider all possible samples of size two which can be drawn with replacement from this population. Find a) the mean of the population, b) the standard deviation of the population, e) the mean of the sampling distribution of means, d) the standard deviation of the sampling distribution of means. 6. Using the data of Problem 5, compute the mean of the sampling distribution of variances corresponding to the samples drawn.

use sample 1,2,2,5,5 rest stays the same

Answer 1

I72727272 - 2.0 --?- H=272+2=212+2=252+=2763=2) to 0.6324 Beth 2) 12v (2.70 121 122 2 í 12,2 13.1 (32) 62) 12.00 12,2) 12,2 (3,2) (1.2) 12,2) (2,29 (2,2 (3,2) (1,3) (23) (23) (2,3) (3.3) There are 25 two which geplase mento Samples of size can be drawn with The corresponding Sample means are 1.5 a 1.5 Ī 1.5 15 1.5 2 2.5 1.5 2 9 2 2.5 2 2.5 2 2.5 2-5 3 2

And the mean of distribution is More Sum of all sample means abou 25 وت illustrating the fact that Mr = d.) The variance o 2 of the sampling distribution means is obtained by subtracting the mean 2 from each number, squaning the result, adding all 25 numbers obtained and dividine 1 The final result is - 25 5.24 0.2096 -To 5 0.4578 Answred
For this sample data 1,2,2,5,5 same above steps will follow

(a) $\mu$ = $\frac{1+2+2+5+5}{5}$ = 3

(b) standard deviation

$\sigma ^{2}$ = 2.8

$\sigma$ = 1.6733

(c) mean of the sample distribution

$\mu _{x}$ = $\frac{sum of all sample means above}{25}$

$\mu _{x}$ = 75/25 = 3

$\mu _{x}$ = 3

(d)  

Standard Deviation Calculation

N: 25
M: 3
SS: 35
s² = SS⁄(N - 1) = 35/(25-1) = 1.46
s = √s² = √1.46 = 1.21

Variance = 1.45833.

Standard Deviation = 1.2076

ANSWERED

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