Samplling

Question 1

Sampling Distribution of the Mean

Theorem 1
If all possible samples of size n are drawn with replacement from a finite population of size N, then:
The mean of the sampling distribution of means

Answer 1

µ_x ̅ = µ
The variance of the sampling distribution of means is given by:
〖σ^2〗_x ̅ = σ^2/n . . (iii).
Arising from (iii) σ_x ̅ = σ/√n . . . (iv)
Arising from (iv) the standard score Z = (x ̅- µ)/(σ/√n) . . . (v)
V is a value of the standard normal variate

Question 2

Theorem 2
If all possible samples of size n are drawn without replacement from a finite population of size N, then:
The mean=

Answer 2

of the sampling distribution of means µ_x ̅ = µ
The variance of the sampling distribution of means is given by:
〖σ^2〗_x ̅ ((N-n)/(N-1)) σ^2/n
Here, σ_x ̅ = √(((N-n)/(N-1)) ) (σ/√n)

Question 3

How to get no of possible outcomes in sampling

Answer 3

The first was without replacement while the second was with replacement. Without replacement, you are suppose to have NCn means but with replacement you should have N raise to the power n means

Question 4

Standard error of the sampling distribution of means =

Answer 4

Square root of E (x-mean)^2
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Total number of samples