Page 396 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 30: Types of Hypothesis: Null and Alternative, Types of Errors in Testing Hypothesis and Level of Significance

• Many consumer products are required by law to meet specifications set out in documents known Notes
as standards. This is particularly the case when there are issues of consumer safety, such as
with electrical goods, children’s toys or furniture (fire resistance). In less safety-critical cases,
the standards may be permissive rather than obligatory, but manufacturers will often conform
to the standards, and tell consumers so, as an assurance of quality. Many standards are
established internationally and are embodied in documents published by the International
Standards Organization (ISO). Companies based in the UK and other EU countries usually
operate according to ISO standards.
• In making the decision on the basis of sample evidence, the quality controller is taking two
risks. One risk is that a batch meeting the AQL requirement will be incorrectly rejected. The
second risk is that a batch not meeting the AQL requirement will be incorrectly accepted. The
sampling schemes laid down in ISO 4859-1 are intended to clarify and restrict the level of risk
involved, and to strike a sensible balance between the two types of risk.
• In research studies such as these, the null and alternative hypotheses should he formulated so
that the rejection of H supports the research conclusion. The research hypothesis therefore
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should be expressed as the alternative hypothesis.
• In any situation that involves testing the validity of a claim, the null hypothesis is generally
based on the assumption that the claim is true. The alternative hypothesis is then formulated so
that rejection of H will provide statistical evidence that the stated assumption is incorrect.
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Action to correct the claim should be considered whenever H is rejected.
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• In testing research hypotheses or testing the validity of a claim, action is taken if H is rejected.
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In many instances, however, action must be taken both when H cannot be rejected and when
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H can be rejected. In general, this type of situation occurs when a decision-maker must choose
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between two courses of action, one associated with the null hypothesis and another associated
with the alternative hypothesis.
• The hypothesis tests in this unit involve one of two population parameters: the population
mean and the population proportion. Depending on the situation, hypothesis tests about a
population parameter may take one of three forms; two include inequalities in the null
hypothesis, the third uses only an equality in the null hypothesis.
• The hypothesis testing procedure should lead to the acceptance of the null hypothesis H when
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it is true, and the rejection of H when it is not. However, the correct decision is not always
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possible. Since the decision to reject or accept a hypothesis is based on sample data, there is a
possibility of an incorrect decision or error.
• The probability of making a Type I error, is referred to as the level of significance. The probability
level of this error is decided by the decision-maker before the hypothesis test is performed and
is based on his tolerance in terms of risk of rejecting the true null hypothesis. The risk of making
Type I error depends on the cost and/or goodwill loss. The complement ( 1 α of the probability
) −
of Type I error measures the probability level of not rejecting a true null hypothesis. It is also
referred to as confidence level.
• The ability (probability) of a test to reject the null hypothesis when it is false. Often, when the
null hypothesis is false, another alternative value of the population mean, μ is unknown. So
for each of the possible values of the population mean μ , the probability of committing Type II
error for several possible values of μ is required to be calculated.E
• However, if both types of errors are costly, then to keep both α and β low, then inferences can
be made more reliable by reducing the variability of observations. It is preferred to have large
sample size and a low α value.
• However, if both types of errors are costly, then to keep both α and β low, then inferences can
be made more reliable by reducing the variability of observations. It is preferred to have large
sample size and a low α value.

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