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"It has long been an axiom of mine that the little things are infinitely the most important" (Sherlock Holmes)

 

 

Confidence Interval of a Mean Normal approximation method

 

Large sample from an 'infinite' population

Worked example

The mean haemoglobin content for a random sample of 225 school children is 108 g/l with a standard deviation (s) of 41 g/l. The 95% confidence interval is given by:
95% CI()    =    108 ± 1.96 41
√225
     =    102.6 to 113.4  

Hence the range 102.6 to 113.4 g/L should enclose the true mean haemoglobin content on 95% of occasions it is calculated, assuming that range is calculated in a similar fashion from randomly selected samples.

 

Small sample from an 'infinite' population

Worked example

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The mean GBH (girth at breast height) for a random sample of 10 aspen trees is 34.7 cm with a standard deviation (s) of 6.77 cm. A histogram of the frequency distribution suggests that it may be close to normal.

Remember: you will always have less confidence in statistics derived from small samples as they may not be representative of the population.

Bearing this in mind....

The 95% confidence interval is given by:

95% CI()    =    34.7 ± 2.26 6.77
√10
     =    29.9 to 39.5  

Hence the range 29.9 to 39.5 cm should enclose the true mean girth at breast height on 95% of occasions it is calculated, assuming that range is calculated in a similar fashion from randomly selected samples.

 

Sample from a small finite population

Worked example

The mean serum copper content for a random sample of 74 white rhinos out of the total world population of 560 white rhinos is 6.3 μmol/L, with a standard deviation of 2.3 μmol/L. The 95% confidence interval is given by:

95% CI ()   =   6.3 ± 1.96 2.3 √( 1 −74 )
√74560
    =   5.81 to 6.79  

Hence the range 5.81 to 6.79 μmol/L should enclose the true mean serum copper content on 95% of occasions it is calculated, assuming that range is calculated in a similar fashion from randomly selected samples.