- CFA Exams
- 2024 Level I
- Topic 1. Quantitative Methods
- Learning Module 8. Hypothesis Testing
- Subject 2. Null Hypothesis and Alternative Hypothesis

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##### Subject 2. Null Hypothesis and Alternative Hypothesis PDF Download

The

**null hypothesis**(designated H

_{0}) is the statement that is to be tested. The null hypothesis is a statement about the value of a population. The null hypothesis will either be rejected or fail to be rejected.

_{0}, would be written as: H_{0}: μ = 1%._{0}: r_{1}= r_{2}.

It is important to point out that accepting the null hypothesis does not prove that it is true. It simply means that there is not sufficient evidence to reject it.

Note that it makes no sense to hypothesize about known sample values, for the simple reason that they are known, just like it makes no sense to construct confidence intervals or obtain point estimates for known values. Hypothesis tests are carried out on unknown population parameters.

The

**alternate hypothesis**is the statement that is accepted if the sample data provides sufficient evidence that the null hypothesis is false. It is designated as H

_{1}and is accepted if the sample data provides sufficient statistical evidence that H

_{0}is false.

The following example clarifies the difference between the two hypotheses. Suppose the mean time to market for a new pharmaceutical drug is thought to be 3.9 years. The null hypothesis represents the current or reported condition and would therefore be H

_{0}: μ = 3.9. The alternate hypothesis is that this statement is not true, that is, H

_{1}: μ ≠ 3.9. The null and alternative hypotheses account for all possible values of the population parameter.

There are three basic ways of formulating the null hypothesis.

_{0}: μ = μ_{0}versus H_{1}: μ ≠ μ_{0}. This hypothesis is two-tailed, which means that you are testing evidence that the actual parameter may be statistically greater or less than the hypothesized value._{0}: ≤ μ_{0}versus H_{1}: μ > μ_{0}. This hypothesis is one-tailed; it tests whether there is evidence that the actual parameter is significantly greater than the hypothesized value. If there is, the null hypothesis is rejected. If there is not, the null hypothesis is accepted._{0}: μ ≥ μ_{0}versus H_{1}: μ < μ_{0}. This hypothesis is one-tailed; it tests whether there is evidence that the actual parameter is significantly less than the hypothesized value. If there is, the null hypothesis is rejected. If there is not, the null hypothesis is accepted.

The question most likely to be raised at this point is how do you know if a test is one-sided or two-sided? The general rule is as follows:

- If a question makes it clear that only one direction is to be examined, use a one-sided test.
- If there is no clue in the question as to which direction should be examined, use a two-sided test.

Normally, there is little ambiguity; the question will make it clear which test should be used. A question often asked involves testing whether a population mean is greater than or less than a specific number. In this case, use a one-tailed test. If the question asks you to test whether a population mean is different from a specific number, use a two-tailed test.

With practice, you'll see that this issue is not really a huge problem.

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**User Contributed Comments**
3

User |
Comment |
---|---|

uma85 |
Two tailed test-Keyword : Equal One Tailed test-Keyword : Higher or Lower |

DonAnd |
these basic questions should definitely be attempted. They make the concept a whole lot clearer. |

afficionado |
Please take note that the traditional statement, "accept the null hypothesis", has been replaced by "fail to reject the null" |

I am using your study notes and I know of at least 5 other friends of mine who used it and passed the exam last Dec. Keep up your great work!