Page 387 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes courses of action, one associated with the null hypothesis and another associated with the alternative
hypothesis. The quality-testing scenario outlined in the Statistics in Practice at the beginning of the
unit is an example of this.
Suppose that, on the basis of a sample of parts from a shipment just received, a quality control inspector
must decide whether to accept the shipment or to return the shipment to the supplier because it does
not meet specifications. The specifications for a particular part require a mean length of two centimetres
per part. If the mean length is greater or less than the two-centimeter standard, the parts will cause
quality problems in the assembly operation. In this case, the null and alternative hypothesis would
be formulated as follows.
H : μ = 2
0
H : μ ≠ 2
1
If the sample results indicate H cannot be rejected, the quality control inspector will have no reason
0
to doubt that the shipment meets specifications, and the shipment will be accepted. However, if the
sample results indicate H should be rejected, the conclusion will be that the parts do not meet
0
specifications. In this case, the quality control inspector will have sufficient evidence to return the
shipment to the supplier. We see that for these types of situations, action is taken both when H
0
cannot be rejected and when H can be rejected.
0
Summary of forms for null and 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. For hypothesis tests involving a population mean, we let μ denote
0
the hypothesized value and choose one of the following three forms for the hypothesis test.
H : μ μ≥ H : μ μ≤ H : μ = μ
0 0 0 0 0 0
H : μ μ< H : μ > μ H : μ ≠ μ
1 0 1 0 1 0
For reasons that will be clear later, the first two forms are called one-tailed tests. The third form is
called a two-tailed test.
In many situations, the choice of H and H is not obvious and judgment is necessary to select the
0 1
proper form. However, as the preceding forms show, the equality part of the expression (either ≥ ,
≤ or =) always appears in the null hypothesis. In selecting the proper form of H and H , keep in mind
1
0
that the alternative hypothesis is often what the test is attempting to establish. Hence, asking whether
the user is looking for evidence to support μ μ< 0 , μ > μ or μ ≠ μ will help determine H . The
1
0
0
1
following exercises are designed to provide practice in choosing the proper form for a hypothesis
test involving a population mean.
30.2 Types of Errors in Testing Hypothesis
Ideally the hypothesis testing procedure should lead to the acceptance of the null hypothesis H
0
when it is true, and the rejection of H when it is not. However, the correct decision is not always
0
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. A decision-maker may commit two types of errors while testing a
null hypothesis. The two types of errors that can be made in any hypothesis testing are shown in
Table 1.

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