Question

Define the terms **standard error** and **standard deviation**. Then, using a hypothetical example _not in the textbook_, describe a situation in which you could compute the two, and highlight how they are different (hint: your answer should include a description of how to generate a **sampling distribution**).

Answer 1

(1) Standard Error (SE) of a statistic is defined as the Standard deviation of the Sampling Distribution of that statistic and it measures the accuracy with which a sample represents a population.

(2) Standard Deviation (SD) is defined as a quantity expressing by how much the members of a group differ from the mean value for the group.

(3)

EXAMPLE OF STANDARD ERROR:

x	x -	(x - )2
14	-40	1600
36	- 18	324
45	- 9	81
70	16	256
105	51	2601
Total =		4862

Sample Mean () is given by:

Sample Standard Deviation (s) is given by:

So,

Sample Standard Deviation = s = 34.86

Standard Error of mean ( $SE_{ar{x}}$ ) :

So,

Standard Error of Mean = 15.63

(4)

EXAMPLE OF STANDARD DEVIATION:

x	x -	(x - )2
14	-40	1600
36	- 18	324
45	- 9	81
70	16	256
105	51	2601
Total =		4862

Sample Mean () is given by:

Sample Standard Deviation (s) is given by:

So,

Sample Standard Deviation = s = 34.86

(5)

DESCRIPTION OF HOW TO GENERATE A SAMPLING DISTRIBUTION:

Repeated sampling wit replacement for different sample sizes produces sampling distribution of the statistic.