In statistics, the null hypothesis ($H_0$) and the alternative hypothesis ($H_a$) are fundamental concepts used in hypothesis testing.

Null Hypothesis ($H_0$):

• The null hypothesis is a statement that assumes there is no effect, relationship, or difference in the population, or that any observed effect is due to chance.
• It represents the status quo or default position.
• Example: In a study testing the effectiveness of a drug, the null hypothesis might state: The drug has no effect on patients compared to a placebo.

Alternative Hypothesis ($H_a$):

• The alternative hypothesis is a statement that directly contradicts the null hypothesis, suggesting there is an effect, relationship, or difference in the population.
• It represents what the researcher seeks to prove or demonstrate.
• Example: Continuing the drug study, the alternative hypothesis might state: The drug has a significant effect on patients compared to a placebo.

Key Differences:

Aspect	Null Hypothesis ($H_0$)	Alternative Hypothesis ($H_a$)
Purpose	Represents no effect or the default assumption	Represents the effect or relationship being tested
Assumption	Presumed true until evidence suggests otherwise	Tested using data to determine validity
Symbols	$H_0$	$H_a$ or $H_1$

Hypothesis Testing Steps:

1. Define $H_0$ and $H_a$.
2. Collect sample data and calculate a test statistic.
3. Compare the test statistic to a critical value or p-value.
4. Decide whether to reject $H_0$ (supporting $H_a$) or fail to reject $H_0$.

Would you like a more detailed explanation or a practical example of hypothesis testing?

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5 Related Questions:

1. What are common examples of null and alternative hypotheses in real-world research?
2. How do we decide whether to use a one-tailed or two-tailed test for $H_a$?
3. What is the role of the significance level ($\alpha$) in hypothesis testing?
4. Can the null hypothesis ever be proven true?
5. What is the difference between a Type I and Type II error in hypothesis testing?

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Tip:

Always clearly define your null and alternative hypotheses before conducting a test, as this sets the foundation for your statistical analysis.