Null Hypothesis Examples
Example 1: A researcher claims that the average time students spend on homework is 2 hours per night.
Solution:
Null Hypothesis (H0): The average time students spend on homework is equal to 2 hours per night.
Data: A random sample of 30 students has an average homework time of 1.8 hours with a standard deviation of 0.5 hours.
Test Statistic and Decision:
Using a t-test, if the calculated t-statistic falls within the acceptance region, we fail to reject the null hypothesis. If it falls in the rejection region, we reject the null hypothesis.
Conclusion:
Based on the statistical analysis, we fail to reject the null hypothesis, suggesting that there is not enough evidence to dispute the claim of the average homework time being 2 hours per night.
Example 2: A company asserts that the error rate in its production process is less than 1%.
Solution:
Null Hypothesis (H0): The error rate in the production process is 1% or higher.
Data: A sample of 500 products shows an error rate of 0.8%.
Test Statistic and Decision:
Using a z-test, if the calculated z-statistic falls within the acceptance region, we fail to reject the null hypothesis. If it falls in the rejection region, we reject the null hypothesis.
Conclusion:
The statistical analysis supports rejecting the null hypothesis, indicating that there is enough evidence to dispute the company’s claim of an error rate of 1% or higher.
Null Hypothesis
Null Hypothesis, often denoted as H0, is a foundational concept in statistical hypothesis testing. It represents an assumption that no significant difference, effect, or relationship exists between variables within a population. It serves as a baseline assumption, positing no observed change or effect occurring. The null is the truth or falsity of an idea in analysis.
In this article, we will discuss the null hypothesis in detail, along with some solved examples and questions on the null hypothesis.
Table of Content
- What is Null Hypothesis?
- Null Hypothesis Symbol
- Formula of Null Hypothesis
- Types of Null Hypothesis
- Null Hypothesis Examples
- Principle of Null Hypothesis
- How do you Find Null Hypothesis?
- Null Hypothesis in Statistics
- Null Hypothesis and Alternative Hypothesis
- Null Hypothesis and Alternative Hypothesis Examples
- Null Hypothesis – Practice Problems