FIRE EFFECTS GUIDE - National Wildfire Coordinating Group

1 70 4900
2 90 8100
3 80 6400
4 70 4900
5 60 3600
6 80 6400
7 90 8100
8 100 10000
9 90 8100
10 80 6400
11 70 4900
12 60 3600
n =
12
Êx = 940
Ê x 2 =
75,400
Note that the Ê symbol means summation.
a. Step 1. Look up t value from t table in most statistical texts (e.g.,
Freese 1967, p. 77). Degrees of freedom (df) are n - 1 (12 - 1 = 11). The
appropriate t value at the 90 percent confidence level (or 10 percent
error rate) is 1.796.
b. Step 2. Calculate the variance (s 2 ) of the preliminary, 12-observation
sample according to [note that this calculation results in the sample
variance (s 2 ) rather than the sample standard deviation (s)]:
s 2 = Êx 2 - ((Êx) 2 /n) / n-1 = 75,400 - ((940) 2 / n) / 11 = 160.6
c. Step 3. Decide how much error can be tolerated. In this example, the
manager wanted the estimate to be within 10 percentage points of the
true mean moisture content. Therefore, E = 10.
d. Step 4. Calculate the appropriate sample size according to the
formula described above:
n = (t 2 s 2 ) / E 2 = (1.796) 2 (160.6) / (10) 2 = 5.18 = 6 observations