6. Hypothesis Testing Flashcards
What is a hypothesis?
A hypothesis is a statement about the value of a population parameter developed for the purpose of testing a theory or belief. Hypotheses are stated in terms of the population parameter to be tested, like the population mean, µ.
For example, a researcher may be interested in the mean daily return on stock options. Hence, the hypothesis may be that the mean daily return on a portfolio of stock options is positive.
What is the hypothesis testing procedure?
What is a null hypothesis?
Null hypothesis: designated H0, is the hypothesis that the researcher wants to reject. It is the hypothesis that is actually tested and is the basis for the selection of the test statistics.
What is an alternative hypothesis?
Alternative hypothesis: designated Ha, is what is concluded if there is sufficient evidence to reject the null hypothesis. It is usually the alternative hypothesis that you are really trying to assess.
What is a one-tailed hypothesis test?
A one-sided test is referred to as a one-tailed test.
If a researcher wants to test whether the return on stock options is greater than zero, a one-tailed test should be used.
What is a two-tailed hypothesis test?
A two-sided test is referred to as a two-tailed test.
A two-tailed test should be used if the research question is whether the return on options is simply different from zero.
How is a two-tailed test for the population mean structured?
What is the decision rule for rejecting?
Example of two-tailed test
Two Tailed Test Graph
How is a one-tailed test for the population mean structured?
What is the decision rule for rejecting?
Example of one-tailed test
One Tailed Test Graph
How to choose between Null and Alternative Hypotheses?
The most common null hypothesis will be an “equal to” hypothesis. Combined with a “not equal to” alternative, this will require a two-tailed test.
When the null is less than or equal to, the (mutually exclusive) alternative is framed as greater than, and a one-tail test is appropriate. If we are trying to demonstrate that a return is greater than the risk-free rate, this would be the correct formulation.
What is a test statistic?
The test statistic is the difference between the sample statistic and the hypothesized value, scaled by the standard error of the sample statistic. Hypothesis testing involves two statistics: the test statistic calculated from the sample data and the critical value of the test statistic. The value of the computed test statistic relative to the critical value is a key step in assessing the validity of a hypothesis.
Test Statistic equation:
