Sampling distribution of mean

• Describes possible outcomes i.e. mean or mode of some variables.
• When the population is normally distributed, then

a) Shape is normally distributed

b) Same size doesn’t affect the center of distribution

• Sampling distribution depends on:

a) Sampling procedure

b) Statistics

c) Use of sample size

mathematically,

Sample size ( n) = Z²Pq/d²

Where,

n = sample size

z = 1.96

p = 0.5

q = 1-p

d = 0.05 ( Absolute precision or accuracy)

Note:

a. Spread or standard error:

SE =σ/   where, σ = Standard deviation and n = no. of sample.

b. Standardizing a sample mean ( Standard Normal distribution)

Standardized sample mean (z) = x-µ/ σ

Where, z = standard score, x= observed value , µ = mean of the sample and σ = standard deviation of the sample