4.8          A population of 12,000 elements has a mean of 100 and a standard deviation of 60. Find the mean and standard error of the sampling distribution of the mean for sample sizes of (a) 100 and (b) 900.

ðaÞ

 

µX- ¼ µ ¼ 100

 

a         60

aX- ¼ pffinffiffi ¼ pffi1ffiffi0ffiffi0ffiffiffi ¼ 6

 

ðbÞ

 

µX- ¼ µ ¼ 100

Since a sample of 900 is more than 5% of the population size, the finite correction factor must be used in the formula for the standard    error:

 

 

 

  a   rffiNffiffiffiffiffi-ffiffiffiffinffiffiffi

 

   

   60    sffi1ffiffi2ffiffi,ffiffi0ffiffi0ffiffi0ffiffiffiffiffiffiffiffiffi9ffiffi0ffiffi0ffiffiffi               sffiffiffiffiffiffiffiffiffiffiffiffiffiffi          p

 

-             60

p

 

11,100

 

2    ffi0ffiffi:ffi9ffiffiffi2ffiffi5ffiffi

 

2 0:962

 

1:92

 

aX- ¼ pffinffiffi

 

N - 1 ¼

 

ffi9ffiffi0ffiffi0ffiffiffi

 

12,000 - 1

 

¼ 30

 

11,999 ffi

 

ffi   ð          Þ ffi

 

 

Without the correction factor, aX- would have been equal to 2 instead of 1.92.