Page 358 - DMTH404_STATISTICS

Statistics

Notes Apart from normal distribution, there are certain other probability distributions that are useful
in sampling theory. These distributions are:

2
c
1. Chi - square ( ) distribution.
2. Student's t - distribution.
3. Snedecor's F - distribution.

24.4 Summary

 Let P , P ...... P denote the observations on N units of a population and X , X ...... X be a
1 2 N 1 2 n
simple random sample of size n from it.
A parameter is a measure computed from the observation of the population. For example:

P + P +  + P N
2
1
Population Mean ( ) m = ,
N
1 2
2
Population Variance ( ) = å ( i ) m , etc. are parameters.
s
P -
N
In a similar way, a statistics is a measure computed from the observations of a sample. For
example:
X + X +  + X n
2
1
X
Sample Mean ( ) = ,
n
1 2
2
S
Sample Variance ( ) = å ( X - X ) , etc. are statistic.
i
n
 The standard deviation of a statistic is termed as standard error. The standard error of X ,
s
to be written in abbreviated form as S.E. X d i, is equal to , when sampling is with
n
s N n
-
replacement and it is equal to × , when sampling is without replacement.
n N 1
-
 S.E. X d i is inversely related to the sample size.
N n
-
 The term is termed as finite population correction (fpc). We note that fpc tends to
-
N 1
become closer and closer to unity as population size becomes larger and larger.
24.5 Keywords

Theoretical probability: A theoretical probability distribution is constructed on the basis of the
specification of the conditions of a random experiment.
Parameter: A parameter is any function of population values while a statistic is a function of
sample values.

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