Question

• A population of scores is normally distributed with a standard deviation equal to 6. State whether the standard error will increase, decrease, or remain unchanged if the value of the population standard deviation is changed to the following.
• 
  
• 
  
• 
  

• Part (a)

  σ = 8

  The standard error will increase.

• The standard error will decrease.    

• The standard error will remain unchanged.

• Part (b)

  σ =

  18

  3

  The standard error will increase.

• The standard error will decrease.    

• The standard error will remain unchanged.

• Part (c)

  σ = 3

  The standard error will increase.

• The standard error will decrease.    

• The standard error will remain unchanged.

• Part (d)

  σ =

  3

  12

  The standard error will increase.

• The standard error will decrease.    

• The standard error will remain unchanged.

• Part (e)

  σ = 6.5

  The standard error will increase.

• The standard error will decrease.    

• The standard error will remain unchanged.

• Part (f)

  σ = 0

  The standard error will increase.

• The standard error will decrease.   

• The standard error will remain unchanged.

Answer 1

Please don't hesitate to give a "thumbs up" for the answer in case the answer has helped you

There are a couple of mis-prints in the question on the sigma values in b) and d). Please let me know if I've assumed correctly in the below answer. If not either write back with the correct Sigma in part b and d) or you can apply the very simple concept explained below.

Simple concept:

Standard error is basically = Standard deviation divided by sqrt(n)

= Sigma/sqrt(n)

So, if standard deviation decreases, Standard error decreases
So, if standard deviation inreases, Standard error increases

Original value = 6

a. Sigma increased to 8
Answer: The standard error will increase.

b. Sigma = 18 ( is it 18 ? please confirm ). If it is 18, Sigma increased
Answer: The standard error will increase.

c. Sigma decreased to 3
Answer: The standard error will decrease.

d. Sigma = 12 ( is it 12 ? please confirm ). If it is 12, Sigma increased
Answer: The standard error will increase.

e. Sigma increased to 6.5
Answer: The standard error will increase.

f. Sigma decreased to 0, standard error would become 0
Answer: The standard error will decrease.