**Quantitative Methods: Application**

**Reading 11. Hypothesis Testing**

**Learning Outcome Statements**

a. define a hypothesis, describe the steps of hypothesis testing, and describe and interpret the choice of the null and alternative hypotheses;

*CFA Curriculum, 2020, Volume 1*

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### Subject 1. Introduction

**hypothesis**is a statement about a population created for the purpose of statistical testing. All hypothesis tests involve making statements about population parameters, or population distributions, and testing those statements based on samples taken from the population to see whether the statements are true.

Examples of hypotheses made about a population parameter are:

- The mean monthly income for a financial analyst is $5,000.
- 25% of R&D costs are ultimately written off.
- 19% of net income statements are later found to be materially incorrect.

Testing a Hypothesis

**State the Null Hypothesis and the Alternate Hypothesis**

The first step is to state the**null hypothesis**(designated: H_{0}), which 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.**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.**Determine the Appropriate Test Statistic and its Probability Distribution**

A**test statistic**is simply a number, calculated from a sample, whose value, relative to its probability distribution, provides a degree of statistical evidence against the null hypothesis. In many cases, the test statistic will not provide evidence sufficient to justify rejecting the null hypothesis. However, sometimes the evidence will be strong enough so that the null hypothesis is rejected and the alternative hypothesis is accepted instead.

Typically, the test statistic will be of the general form:

test statistic = (sample statistic - parameter value under H_{0}) / standard error of sample statistic**Select the Level of Significance**

After setting up H_{0}and H_{1}, the next step is to state**the level of significance**, which is the probability of rejecting the null hypothesis when it is actually true.**Alpha**is used to represent this probability. The idea behind setting the level of significance is to choose the probability that a decision will be subject to a Type I error. There is no one level of significance that is applied to all studies involving sampling. A decision by the researcher must be made to use the 0.01 level, 0.05 level, 0.10 level, or any other level between 0 and 1. A lower level of significance means that there is a lower probability that a Type I error will be made.**Formulate the Decision Rule**

A**decision rule**is a statement of the conditions under which the null hypothesis will be rejected and under which it will not be rejected.

The**critical value**(or rejection point) is the dividing point between the region where the null hypothesis is rejected and the region where it is not rejected. The region of rejection defines the location of all those values that are so large (in absolute value) that the probability of their occurrence is low if the null hypothesis is true.**Collect the Data, Perform Calculations**

Once the data is collected, the test statistic should be calculated.**Making a Decision**

If the test statistic is greater than the higher critical value (or, in a two-tailed test, less than the lower critical value), then the null hypothesis is rejected in favor of the alternative hypothesis.**Making an Investment Decision**

Making an investment decision (or economic decision) entails not just the use of statistical decision algorithms but economic considerations as well.

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**User Contributed Comments**
4

You need to log in first to add your comment. ###### rfvo

These also represent the criterias for selecting estimation samples and further more Hypothesis tests.

###### JakeZ

Alpha = False Negative no?

###### Mosobalaje

Null hypothesis will always have some kind of "=" sign. It could also be testing that something is greater than or equal to/less then or equal to.

###### afficionado

Mosobalaje, the Null hypothesis will not always have some kind of "=" sign since it can also have the "<, < or equal to, >, or > or equal to" sign, depending on what is being tested