The alternative hypothesis (H₁) in statistical hypothesis testing stands in opposition to the null hypothesis (H₀). It is the hypothesis that researchers aim to support. If the sample data provide sufficient evidence, it leads to the rejection of the null hypothesis in favor of the alternative hypothesis. This hypothesis is what a researcher typically expects to conclude based on the study or experiment performed.
Examples
-
Medical Research:
- Null Hypothesis (H₀): The new drug has no effect on patients.
- Alternative Hypothesis (H₁): The new drug lowers blood pressure in patients.
-
Market Research:
- Null Hypothesis (H₀): Customer satisfaction levels have not changed after introducing the new feature.
- Alternative Hypothesis (H₁): Customer satisfaction levels have improved after introducing the new feature.
Frequently Asked Questions
What is the purpose of the alternative hypothesis?
The alternative hypothesis provides a statement that indicates the existence of an effect or difference. It helps researchers determine if their predictions and theories can be supported by data.
How is the alternative hypothesis represented?
The alternative hypothesis is generally represented by H₁ or H_a.
When is the alternative hypothesis accepted?
The alternative hypothesis is accepted when there is sufficient evidence in the sample data to reject the null hypothesis.
What is the relationship between the null hypothesis and the alternative hypothesis?
The null hypothesis and the alternative hypothesis are mutually exclusive and collectively exhaustive. Acceptance of the alternative hypothesis implies the rejection of the null hypothesis, and vice versa.
Can the alternative hypothesis predict a specific direction?
Yes, alternative hypotheses can be one-sided (e.g., specifying a particular direction such as “greater than”) or two-sided (e.g., indicating a difference without specifying the direction).
- Null Hypothesis (H₀): The hypothesis that there is no significant difference or effect.
- p-value: Measures the probability of observing the sample data, or something more extreme, assuming the null hypothesis is true.
- Type I Error: The rejection of a true null hypothesis (false positive).
- Type II Error: The failure to reject a false null hypothesis (false negative).
- Statistical Significance: The likelihood that the observed association or effect is not due to chance.
Online References
Suggested Books for Further Studies
- “Introduction to the Practice of Statistics” by David S. Moore, George P. McCabe, and Bruce A. Craig
- “The Art of Statistics: How to Learn from Data” by David Spiegelhalter
- “Hypothesis Testing Made Simple” by De Haan B
Fundamentals of Alternative Hypothesis: Statistics Basics Quiz
### What does the alternative hypothesis represent in hypothesis testing?
- [x] It represents an effect or difference that is contrary to the null hypothesis.
- [ ] It represents no effect or no difference.
- [ ] It always predicts the exact opposite outcome of the null hypothesis.
- [ ] It is unnecessary in hypothesis testing.
> **Explanation:** The alternative hypothesis represents a statement indicating the existence of an effect or difference contrary to the null hypothesis.
### In which of the following cases might the alternative hypothesis be accepted?
- [x] When the sample data provides sufficient evidence to reject the null hypothesis.
- [ ] When the sample data exactly matches the null hypothesis.
- [ ] When there is no data available.
- [ ] When statistical analyses are not performed.
> **Explanation:** The alternative hypothesis is accepted when there is sufficient evidence in the sample data to reject the null hypothesis.
### How is the alternative hypothesis typically denoted?
- [ ] H₀
- [x] H₁
- [ ] Hₙ
- [ ] Hₐ
> **Explanation:** The alternative hypothesis is typically denoted by H₁ or Hₐ.
### Which statement best describes a one-sided alternative hypothesis?
- [x] It specifies a particular direction, such as "greater than" or "less than."
- [ ] It indicates no direction at all.
- [ ] It makes no assumptions about the null hypothesis.
- [ ] It can only be used in non-statistical scenarios.
> **Explanation:** A one-sided alternative hypothesis specifies a particular direction (e.g., greater than or less than).
### What error is made if the null hypothesis is not rejected when it is actually false?
- [ ] Type I Error
- [x] Type II Error
- [ ] Null Error
- [ ] Sampling Error
> **Explanation:** A Type II Error occurs when the null hypothesis is not rejected even though it is actually false.
### What is a two-sided alternative hypothesis?
- [x] It indicates a difference without specifying the direction.
- [ ] It specifies a specific direction of difference.
- [ ] It always results in rejection of the null hypothesis.
- [ ] It avoids comparison with the null hypothesis.
> **Explanation:** A two-sided alternative hypothesis indicates a difference without specifying the direction.
### When is p-value critical for accepting the alternative hypothesis?
- [ ] Only when the p-value is above the critical level.
- [ ] The p-value is irrelevant to the alternative hypothesis.
- [x] When the p-value is below the predetermined significance level, indicating strong evidence against the null hypothesis.
- [ ] When it confirms no difference.
> **Explanation:** The p-value is critical because, when it is below the predetermined significance level, it indicates strong evidence against the null hypothesis, which can lead to accepting the alternative hypothesis.
### What is the outcome for hypothesis testing when a Type I Error occurs?
- [x] A true null hypothesis is rejected.
- [ ] A true null hypothesis is accepted.
- [ ] A true alternative hypothesis is rejected.
- [ ] A true alternative hypothesis is accepted.
> **Explanation:** A Type I Error involves the rejection of a true null hypothesis.
### Why is the alternative hypothesis important?
- [x] It provides a basis for testing and predicting an effect or difference.
- [ ] It counteracts the null hypothesis with weak evidence.
- [ ] It validates the null hypothesis.
- [ ] It simplifies the process of statistical testing.
> **Explanation:** The alternative hypothesis provides a basis for testing and predicting an effect or difference, leading to meaningful conclusions in research.
### What is the main goal of hypothesis testing?
- [ ] To prove the null hypothesis correct.
- [ ] To complicate data analysis.
- [x] To assess evidence against the null hypothesis in order to support the alternative hypothesis.
- [ ] To invalidate all competing hypotheses.
> **Explanation:** The main goal of hypothesis testing is to assess evidence against the null hypothesis to support the alternative hypothesis.
Thank you for exploring the concept of the alternative hypothesis and completing our challenging sample exam quiz questions. Keep advancing in your statistical knowledge!
