For the following questions, assume a normally distributed population. [5 points

Question

For the following questions, assume a normally distributed population. [5 points]

                  a. Given =50, =36, and n=25, compute the standard error of the mean.

                  b. Given =50, =36, and n=900, compute the standard error of the mean.

                  c. Given =50, =4, and n=25, compute the standard error of the mean.

                  d. Given =500, =36, and n=25, compute the standard error of the mean.

e. How does the standard error of the mean change when the population mean, population standard deviation, and sample size change?

Explanation / Answer

a.
Mean ( u ) =50
Standard Deviation ( sd )=36
Number ( n ) = 25
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
Standard Error = 36/ Sqrt ( 25 ) = 7.2

b.
Number ( n ) = 900
Standard Error = 36/ Sqrt ( 900 ) = 1.2

c.
Mean ( u ) =50
Standard Deviation ( sd )=4
Number ( n ) = 25
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
Standard Error = 4/ Sqrt ( 25 ) = 0.8

d.
Mean ( u ) =500
Standard Deviation ( sd )=36
Number ( n ) = 25
Standard Error = 36/ Sqrt ( 25 ) = 7.2

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