The NormalConfidence XML Web service calculates the confidence intervals for sample means and sample proportions when large samples (i.e > 30 elements) of the entire population are considered.
For a list of all members of this type, see NormalConfidence Members.
System.Object
NormalConfidence
The XML Web service was designed to compute confidence intervals when large
samples (i.e. samples with over 30 elements) are taken from
populations that is normally or near-normally distributed. Since the sample
is large we are able to use a Normal distribution to model populations standard
deviation from the samples to calculate the critical values.
Remark: If the sample size is small (i.e. less than 30
elements), then for confidence intervals of 'means' and related constants can
be evaluate using the StudentConfidence XML Web service instead.
An interval estimate, or a confidence interval, is an interval of values with a given probability of covering the true population parameter. This parameter could be a mean, a proportion or similar point wise statistic.
The mean, or proportion of a sample will seldom exactly equal the corresponding population mean, or population proportion. However, one would expect the statistic of the sample to be approximately equal to the same statistic for the entire population for most samples considered. However, the point wise estimate (i.e. mean or proportion) alone does not give any idea of the magnitude of the possible sampling error. Confidence intervals perform exactly this role and provide a convenient way of indicating the general magnitude of the sampling error for a given level of confidence.
Where there is a large degree of sampling error, the confidence interval estimated from any sample will be large; the range of values likely to cover the population parameter is wide. On the other hand, if the sampling error is small the parameter is likely to be covered by a small estimated range of values.
A confidence interval takes the following form:( statistic(x) - (z * s) , statistic(x) + (z * s) ),
where statistic(x) is the sample parameter, z is known
as the critical value and depends on the confidence level (p) and
s will be the samples standard error. The probability of the population
parameter lying in the interval (statistic(x) - (z * s), statistic(x) - (z * s))
is known as the confidence level (denoted below by p). That is, the
confidence interval claims that the true population parameter (which generally we
do not know) will lie within z standard errors of the sample statistic
with a p percent level of confidence.
Namespace: Hypothesis
Assembly: WebCab.DelphiWebServices.Statistics (in WebCab.DelphiWebServices.Statistics.dll)
NormalConfidence Members | Hypothesis Namespace