Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

T o natio, a, of total miscellaneous delays per year to total yearly
ruaning time is defined:
Note also that t o =
a = t It .
o r
(1..42)
cit . Since the previous analysis permits the es-
timation of T r' which is the point-to-point counterpart of t r , an
.!stimate of miscellaneous delay time expected to be encountered on
any given trip, T o , is
T o = aT r . (4.43)
The factor of proportionality, a, must be estimated from the aggregate
delay data. Note that t o and t r are available from the aggregate data
for each of the 59 boat-year observations. A sample of a's, defined
as in Equation (4.42), are therefore available.
The central limit theorem leads one to believe that the distri-
bution of a should be approximately normal, for miscellaneous delays
are the sum of seven independent random variables. The data were .
tested for normality with a standard chi-square test employing seven
cells. With four degrees of freedom, the calculated statistic is
0.12; the statistic would have to exceed 9.49 for significance of
conventional levels. Therefore, it is concluded that the distribu-
tion of miscellaneous delays is not significantly different from
normal. .
,
Given a normally 'distributed random variable, probably the best
estimate of the mean for most purposes is the sample arithmetic mean.
I., .
ILI