Page 397 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes • An alternative approach to hypothesis testing follows the following steps: specify the null and
alternative hypotheses, specify a value for α , collect the sample data, and determine the weight
of evidence for rejecting the null hypothesis. This weight, given in terms of a probability, is
called the level of significance (or p-value) of the statistical test. More formally, the level of
significance is defined as follows: the probability of obtaining a value of the test statistic that is as
likely or more likely to reject H as the actual observed value of the test statistic, assuming that the null
0
hypothesis is true. Thus, if the level of significance is a small value, then the sample data fail to
support H and our decision is to reject H . On the other hand, if the level of significance is a
0
0
large value, then we fail to reject H . We must next decide what is a large or small value for the
0
level of significance.
30.5 Key-Words
1. Harmonic mean : The number of elements to be averaged divided by the sum of
the reciprocals of the elements.
2. Heavy tailed distribution : A distribution with a higher percentage of scores in the tails than
we would expect in a normal distribution.
3. Heterogeneity of variance : A situation in which samples are drawn from populations having
different variances.
30.6 Review Questions

1. What is meant by the terms hypothesis and a test of a hypothesis ?
2. What do you understand by null hypothesis and alternative hypothesis ? Explain developing
null and alternative hypothesis.
3. Discuss the types of errors in testing hypothesis.
4. Define term 'level of significance'. How is it related to the probability of committing a Type I
error.
5. How is power related to the probability of making a Type II error ?
Answers: Self-Assessment
1. (i) Null (ii) type I (iii) type II
(iv) significance (v) single
30.7 Further Readings

1. Elementary Statistical Methods; SP. Gupta, Sultan Chand & Sons,
New Delhi - 110002.
2. Statistical Methods — An Introductory Text; Jyoti Prasad Medhi, New Age
International Publishers, New Delhi - 110002.
3. Statistics; E. Narayanan Nadar, PHI Learning Private Limied, New Delhi - 110012.
4. Quantitative Methods—Theory and Applications; J.K. Sharma, Macmillan
Publishers India Ltd., New Delhi - 110002.

392 LOVELY PROFESSIONAL UNIVERSITY