Discuss the below:
Q1. Given the following population data: 1,2,4,5,8,9,12, and the lists of all samples of size 2 and 5:
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Samples of n = 2
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xbar
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1,2
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1.5
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1,4
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2.5
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1,5
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3
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1,8
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4.5
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1,9
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5
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1,12
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6.5
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2,4
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3
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2,5
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3.5
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2,8
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5
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2,9
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5.5
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2,12
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7
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4,5
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4.5
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4,8
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6
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4,9
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6.5
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4,12
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8
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5,8
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6.5
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5,9
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7
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5,12
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8.5
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8,9
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8.5
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8,12
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10
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9,12
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10.5
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Samples of
n = 5
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xbar
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1,2,4,5,8
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4
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1,2,4,5,9
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4.2
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1,2,4,5,12
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4.6
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1,2,4,8,9
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4.8
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1,2,4,8,12
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5.4
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1,2,4,9,12
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5.6
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1,2,5,8,9
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5
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1,2,5,8,12
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5.6
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1,2,5,9,12
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5.8
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1,2,8,9,12
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6.4
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1,4,5,8,9
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5.4
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1,4,5,8,12
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6
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1,4,5,9,12
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6.2
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1,4,8,9,12
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6.8
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1,5,8,9,12
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7
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2,4,5,8,9
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5.6
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2,4,5,8,12
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6.2
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2,4,5,9,12
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6.4
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2,5,8,9,12
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7.2
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4,5,8,9,12
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7.6
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2,4,8,9,12
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7
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For population
s = ?
m = ?
For n = 2
sxbar = ?
mxbar = ?
For n = 5
sxbar = ?
mxbar = ?
a) Use Excel to find the six ? values above.
b) Consider the three values of mean and the three values of standard deviation in a). Verify (mathematically) that the Central Limit Theorem applies using the formulas:
µ = µxbar and σxbar = σ / √n
c) Why are your answers from a) and b) slightly off?