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UNIT V
THEORY OF SAMPLING
ENGINEERING MATHS III
QUSTION BOOK
1
UNIT5
THEORY OF SAMPLING
AND TEST OF HYPOTHESIS
Population:
The group of individuals, under study is called is called population.
Sample
:
A finite subset of statistical individuals in a population is called Sample.
Sample size
:
The number of individuals in a sample is called the Sample size.
Parameters and Statistics:
The statistical constants of the population are referred as Parameters and the
statistical constants of the Sample are referred as Statistics.
Standard Error
:
The standard deviation of sampling distribution of a statistic is known as its
standard error and is denoted by (S.E)
Test of Significance
:
It enable us to decide on the basis of the sample results if the deviation between the
observed sample statistic and the hypothetical parameter value is significant or the
deviation between two sample statistics is significant.
Null Hypothesis
:
A definite statement about the population parameter which is usually a hypothesis
of nodifference and is denoted by H
o.
Alternative Hypothesis
:
Any hypothesis which is complementary to the null hypothesis is called an
Alternative Hypothesis and is denoted by H
1.
Errors in Sampling:
Type I and Type II errors.
Type I
error : Rejection of H
0
when it is true.
Type II error : Acceptance of H
0
when it is false.
Two types of errors occurs in practice when we decide to accept or reject a
lot after examining a sample from it. They are Type 1 error occurs while rejecting
H
o
when it is true. Type 2 error occurs while accepting H
o
when it is wrong.
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View Full DocumentUNIT V
THEORY OF SAMPLING
ENGINEERING MATHS III
QUSTION BOOK
2
Critical region:
A region corresponding to a statistic t in the sample space S which lead to the
rejection of H
o
is called Critical region or Rejection region. Those regions which
lead to the acceptance of H
o
are called Acceptance Region.
Level of Significance
:
The probability α that a random value of the statistic “t” belongs to the critical
region is known as the level of significance. In otherwords the level of significance
is the size of the type I error. The levels of significance usually employed in testing
of hypothesis are 5% and 1%.
One tail and two tailed test:
A
test
of
any
statistical
hyposthesis
where
the
alternate
hypothesis
is
one
tailed(right tailed/ left tailed) is called one tailed test.
For the null hypothesis H
0
if µ = µ
0
then.
H
1
= µ > µ
0
(Right tail)
H
1
=
µ < µ
0
(Left tail)
H
1
=
µ # µ
0
(Two tail test)
Types of samples :
Small sample and Large sample
Small sample (n≤<30 ) : “Students t test, F test , Chi Square test
Large sample (n>30)
: Z test.
95 % confidence limit for the population mean
μ
in a small test.
Let x be the sample mean and n be the sample size. Let s be the sample S.D.
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 Spring '06
 Sharma

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