Estimation Theory

Estimation Theory
l A researcher may wish or interest in estimating
population parameters such as (mean,
proportion, variance, etc.)
l Two types of estimate:
1- A point estimate: Is a single numerical value
used to estimate the corresponding population
parameter. For example a sample mean, , is
unbiased estimate of population mean, (?), but
it does not necessarily equal to (?). This type
was pervious explained.
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2- An interval estimate: An estimate of population
parameter given by two numbers between which the
parameter may be considered to lie is called an interval
estimate.
Confidence Interval for Mean, ?, when ? is Known, (C.I):
In repeated sampling, from a normally distributed
population, (1 - a ) 100% of all intervals of the form,
will in the long run include the population mean, ?.
Example: The population standard deviation of SBP of
normal adult males, 25 years old is 15 mm Hg, a sample
of 100 had a mean of SBP of 125 mm Hg. Construct
95% C.I for ?, (? = true population mean of SBP).
l 95% C.I for (m= true population mean of SBP) is,