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There are two types of statistical hypothesis
(i) Null hypothesis (ii) Alternative hypothesis

**Meaning : Null
Hypothesis and Alternative Hypothesis - Level of Significants and Type of
Errors**

Statistical hypothesis
is some assumption or statement, which may or may not be true, about a
population.

There are two types of
statistical hypothesis

(i) Null hypothesis
(ii) Alternative hypothesis

According to Prof.
R.A.Fisher, “Null hypothesis is the hypothesis which is tested for possible
rejection under the assumption that it is true”, and it is denoted by *H*_{0}
.

For example: If we
want to find the population mean has a specified value *μ*_{0} , then the null
hypothesis *H*_{0} is set as follows *H*_{0} : *μ = μ*_{0 }

Any hypothesis which is
complementary to the null hypothesis is called as the alternative hypothesis
and is usually denoted by *H*_{1} .

For example: If we want
to test the null hypothesis that the population has specified mean *μ* i.e., *H*_{0}
: *μ* = *μ*_{ 0} then the alternative
hypothesis could be any one among the following:

i.
*H*_{1} : *μ* ≠ *μ*_{ 0} (*μ* > or *μ* < *μ*_{ 0})

ii.
*H*_{1}* *:* **μ** *>* **μ*_{ 0}

iii.
*H*_{1}* *:* **μ** *<* **μ*_{ 0}

The alternative
hypothesis in *H*_{1} : *μ* ≠ *μ*_{ 0} is known as two tailed
alternative test. Two tailed test is one where the hypothesis about the
population parameter is rejected for the value of sample statistic falling into
either tails of the sampling distribution. When the hypothesis about the
population parameter is rejected only for the value of sample statistic falling
into one of the tails of the sampling distribution, then it is known as
one-tailed test. Here *H*_{1} : *μ* > *μ*_{ 0} and *H*_{1} : *μ* < *μ*_{0}* *are known as one tailed alternative.

Right tailed test: *H*_{1}
: *μ* > *μ*_{ 0} is said to be right
tailed test where the rejection region or critical region lies entirely on the
right tail of the normal curve.

Left tailed test: *H*_{1}
: *μ* < *μ*_{ 0} is said to be left
tailed test where the critical region lies entirely on the left tail of the
normal curve. (diagram)

There is every chance
that a decision regarding a null hypothesis may be correct or may not be
correct. There are two types of errors. They are

Type I error: The error
of rejecting *H*_{0} when it is true.

Type II error: The error
of accepting when *H*_{0} it is false.

A region corresponding
to a test statistic in the sample space which tends to rejection of *H*_{0}
is called critical region or region of rejection.

The probability of type
I error is known as level of significance and it is denoted by . The level of
significance is usually employed in testing of hypothesis are 5% and 1%. The
level of significance is always fixed in advance before collecting the sample
information.

The value of test
statistic which separates the critical (or rejection) region and the acceptance
region is called the critical value or significant value. It depend upon

(i) The level of
significance

(ii) The alternative
hypothesis whether it is two-tailed or single tailed.

For large samples, the
standardized variable corresponding to the statistic viz.,

The value of *Z*
given by (1) under the null hypothesis is known as test statistic. The critical
values of *Z* at commonly used level of significance for both two tailed
and single tailed tests are given in the normal probability table (Refer the
normal probably Table).

Since for large n,
almost all the distributions namely, Binomial, Poisson, etc., can be
approximated very closely by a normal probability curve, we use the normal test
of significance for large samples.

Tags : Statistical Inference , 12th Business Maths and Statistics : Chapter 8 : Sampling Techniques and Statistical Inference

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12th Business Maths and Statistics : Chapter 8 : Sampling Techniques and Statistical Inference : statistical hypothesis: Null Hypothesis and Alternative Hypothesis, Level of Significants, Type of Errors | Statistical Inference

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