 
Confidence Interval of a Mean
Normal approximation method
Large sample from an 'infinite' population
Small sample from an 'infinite' population
Worked example
{Fig. 1}
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
