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Statistical Methods in Economics

Notes (b) Alternative Hypothesis: The alternative hypothesis specifies those values that the researcher believes
to hold true and hopes that the sample data would lead to acceptance of this hypothesis to be true.
The alternative hypothesis may embrace the whole range of values rather than single point.
As per this definition, it is very difficult to find out which is null hypothesis and which one is
alternative hypothesis.
However, for statistical convenience, the hypothesis these definitions are used.
The null hypotheses are represented by the symbol H and the alternative hypothesis is
0
represented by H .
1
Developing null and alternative hypotheses
In some applications it may not be obvious how the null and alternative hypotheses should be
formulated. Care must be taken to structure the hypotheses appropriately so that the conclusion
from the hypothesis test provides the information the researcher or decision-maker wants. Learning
to formulate hypotheses correctly will take practice. The examples in this section show a variety of
forms for H and H depending upon the application. Guidelines for establishing the null and
0 1
alternative hypotheses will he given for three types of situations in which hypothesis testing procedures
are commonly used.
Statistics in Practice
Monitoring the quality of latex condoms
Many consumer products are required by law to meet specifications set out in documents known 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.
The humble latex condom is the subject of ISO standard 4074: 2002. This lays down a range of
specifications, relating to materials, dimensions, packaging and performance criteria including, for
obvious reasons, freedom from holes. For an outline of quality testing procedures, read the relevant
pages at www.durex.com, for example. ISO 4047: 2002 makes reference to other standards documents
including frequent references to ISO 4859-1, which lays down specifications for the sampling schemes
that must be used to ensure quality, such as in respect of freedom from holes, For the latter
characteristic, ISO 4047: 2002 specifies an acceptable quality level (AQL) of no more than 0.25 per
cent defective condoms in any manufacturing batch; in other words, a probability of no more than 1
in 400 that any particular condom will be defective.
As an example of the sampling specifications, suppose ISO 4859-1 requires that, from a batch of
10000 condoms, a random sample of 200 should be taken and examined individually for freedom
from holes. This is likely to be a destructive test. Suppose ISO 4859-1 then stipulates that the whole
batch from which the sample was drawn can be declared satisfactory, in respect of freedom from
holes, only if the sample contains no more than one defective condom. If the sample does contain
more than one defective condom, the whole batch must be scrapped, or further tests of quality must
be done to gather further information about the overall quality of the batch.
A statistician would refer to this decision procedure as a hypothesis test. The working hypothesis is
that the batch conforms to the AQL specified in ISO 4074: 2002.
If the sampled batch contains more than one defective condom, this hypothesis is rejected. Otherwise
the hypothesis is accepted. 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 this chapter you will learn about the logic of statistical hypothesis testing.

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