• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar
  • Skip to footer
Finance Train

Finance Train

High Quality tutorials for finance, risk, data science

  • Home
  • Data Science
  • CFA® Exam
  • PRM Exam
  • Tutorials
  • Careers
  • Products
  • Login

What is Hypothesis Testing

CFA® Exam Level 1, Statistics

Hypothesis Testing What is Hypothesis Testing

Many a times, we want to test the validity of a statement. For example, is the mean return from this mutual fund more to the mean return from the benchmark? While answering such a question, our interest is not to find the actual mean returns of the mutual fund, but to test whether the statement holds true or not.

A hypothesis is a statement about one or more populations like the statement above.

A hypothesis testing is a standard procedure to test the hypothesis. There could be two possible results: 1) The hypothesis is correct and hence should be accepted. 2) The hypothesis is incorrect and should be rejected.

Steps in Hypothesis Testing

The hypothesis testing process consists of the following steps:

  1. Stating the hypotheses.
  2. Identifying the appropriate test statistic and its probability distribution.
  3. Specifying the significance level.
  4. Stating the decision rule.
  5. Collecting the data and calculating the test statistic.
  6. Making the statistical decision.

Null and Alternative Hypothesis

When we form a hypothesis to be tested, the hypothesis is called a null hypothesis. The null hypothesis is written as H0. A null hypothesis will be a simple statement about the population parameter. For example, the hypothesis that the mean returns of a mutual fund will be greater than or equal to 8% will be states as H0: m >= 8%.

The alternative hypothesis is the hypothesis accepted when the null hypothesis is rejected. It is represented as HA. In our example, the alternative hypothesis will be HA: m < 8%.

In general, a hypothesis can be formed as follows:

  1. H0: θ = θ0 versus HA: θ ≠ θ0
  2. H0: θ ≤ θ0 versus HA: θ > θ0
  3. H0: θ ≥ θ0 versus HA: θ < θ0

Where θ represents a population parameter and θ0 is a value assumed in the hypothesis.

One-tailed and Two-tailed Tests

A hypothesis test can be a one-tailed or a two-tailed test. A one-tailed test means that the hypothesis is one-sided such as the second and third formulation above. The second formulation tests whether the population parameter is greater than a certain value (one-sided). The third formulation tests whether the population parameter is greater than a certain value (again one-sided). The first formulation is two-sided; hence the hypothesis test will be twp-tailed. It tests for deviation of value on both sides of θ0.

Example

We will use this example to illustrate the concepts related to hypothesis testing in the following pages.

A portfolio manager believes that the mean returns from a mutual fund are zero. He collects the returns data over the past 100 days and calculate the sample mean returns and the sample standard deviation as follow:

x-bar = 0.2%

s = 0.50%

Based on what we have learned till now, we can state the null and alternative hypothesis as follows:

H0: m = 0 versus HA: m ≠ 0

This is a two-tailed test. We will reject the null hypothesis if the mean is not equal to 0.

Back to Course
Next Lesson

Primary Sidebar

In this Course

Course Home
What is Hypothesis Testing
Test Statistic, Type I and type II Errors, and Significance Level
Decision Rule in Hypothesis Testing
p-Value in Hypothesis Testing
Selecting the Appropriate Test Statistic
Hypothesis Testing with t-statistic
Hypothesis Testing with z-statistic
Tests Concerning Differences in Means
Paired Comparision Tests – Mean Differences When Populations are Not Independent
Hypothesis Tests Concerning Variances
Chi-square Test – Test for value of a single population variance
F-test – Test for the Differences Between Two Population Variances
Non-parametric Tests
Return to Hypothesis Testing

Latest Tutorials

    • Data Visualization with R
    • Derivatives with R
    • Machine Learning in Finance Using Python
    • Credit Risk Modelling in R
    • Quantitative Trading Strategies in R
    • Financial Time Series Analysis in R
    • VaR Mapping
    • Option Valuation
    • Financial Reporting Standards
    • Fraud
Facebook Group

Membership

Unlock full access to Finance Train and see the entire library of member-only content and resources.

Subscribe

Footer

Recent Posts

  • How to Improve your Financial Health
  • CFA® Exam Overview and Guidelines (Updated for 2021)
  • Changing Themes (Look and Feel) in ggplot2 in R
  • Coordinates in ggplot2 in R
  • Facets for ggplot2 Charts in R (Faceting Layer)

Products

  • Level I Authority for CFA® Exam
  • CFA Level I Practice Questions
  • CFA Level I Mock Exam
  • Level II Question Bank for CFA® Exam
  • PRM Exam 1 Practice Question Bank
  • All Products

Quick Links

  • Privacy Policy
  • Contact Us

CFA Institute does not endorse, promote or warrant the accuracy or quality of Finance Train. CFA® and Chartered Financial Analyst® are registered trademarks owned by CFA Institute.

Copyright © 2021 Finance Train. All rights reserved.

  • About Us
  • Privacy Policy
  • Contact Us