Question

Consider a large population with a mean of 150 and a standard deviation of 27. A random sample of size 36 is taken from this population. The standard error of the sampling distribution of sample mean; SE(X) = σx = q V ar(X) is equal to:

Answer 1

SE(X) = σx = 4.5

Var(X) = 20.25

Explanation:

Solution:-

- A large population has a mean ( u ) and standard deviation ( σ ). The parameters of the population distribution are given as follows

u = 150

σ = 27

- A sample of n = 36 people were taken from the population.

- We will first estimate the sample standard deviation (σ) by assuming that the population is normally distributed with conditions :

n ≥ 30

u ≥ 10

- The condition of normality are valid. The population is assumed to be normally distributed. The sample must also be normally distributed. The sample standard deviation (σx):

σx = σ/√n = 27/√36

σx = 4.5 ... sample standard deviation.

- The sample variance can be determined by:

Var ( X ) = ( σx ) ^2

Var ( X ) = ( 4.5 ) ^2

Var ( X ) = 20.25