For each pair of hypotheses that follows, decide whether H₀ and H₁ are set up correctly as the null and alternative hypotheses for a hypothesis test. If so, select “Valid” from the drop down menu. If not, select “Invalid”.
1	H₀: M = 30		2	H₀: μ = 115
H₁: M ≠ 30	    		H₁: μ ≠ 115
3	H₀: μ = 210		4	H₀: µ = 130
H₁: μ ≠ 210	    		H₁: µ ≠ 138
You evaluate the    by assuming that it is true and testing the reasonableness of this assumption by calculating the probability of getting the results if chance alone is operating.

Let��s assess whether the null and alternative hypotheses (H₀ and H��) are correctly set up.

**General guideline for null and alternative hypotheses:**
- **Null hypothesis (H₀):** A statement of no effect, no difference, or a specific claim (usually includes "=").
- **Alternative hypothesis (H₁):** A statement that contradicts H₀, suggesting that there is an effect, difference, or that the value is not equal to the null claim (can include "≠", ">", "<", etc.).

Now, let's analyze the pairs:

---

1. **H₀: M = 30**  
   **H₁: M ≠ 30**

- **Analysis**: 
   - The null hypothesis states that the parameter \(M\) (typically a mean or median) is equal to 30. 
   - The alternative hypothesis contradicts H₀ by stating that \(M\) is not equal to 30.
   - **Verdict: Valid** — This follows the correct structure for a two-tailed test.

---

2. **H₀: μ = 115**  
   **H₁: μ ≠ 115**

- **Analysis**: 
   - The null hypothesis states that the population mean \(μ\) is 115.
   - The alternative hypothesis states that \(μ\) is not equal to 115.
   - **Verdict: Valid** — This is the correct setup for a two-tailed test.

---

3. **H₀: μ = 210**  
   **H₁: μ ≠ 210**

- **Analysis**: 
   - The null hypothesis assumes that the population mean \(μ\) is equal to 210.
   - The alternative hypothesis suggests that the mean is not equal to 210.
   - **Verdict: Valid** — Again, this is correctly set up for a two-tailed test.

---

4. **H₀: µ = 130**  
   **H₁: µ ≠ 138**

- **Analysis**: 
   - The null hypothesis states that the population mean \(μ\) is 130.
   - The alternative hypothesis states that \(μ\) is not equal to **138**. 
   - This is incorrect because the alternative hypothesis must contradict the null hypothesis by involving the **same** value.
   - **Verdict: Invalid** — The correct alternative hypothesis should be \(μ \neq 130\), not \(μ \neq 138\).

---

Thus, the results are:

1. **Valid**
2. **Valid**
3. **Valid**
4. **Invalid**

---

Would you like to explore further details, or do you have any questions? Here are some related questions for further study:

1. What is the difference between a one-tailed and two-tailed hypothesis test?
2. How is the significance level used in hypothesis testing?
3. Why do we always assume the null hypothesis is true when conducting a hypothesis test?
4. Can the null hypothesis contain inequalities like ">" or "<"?
5. How do you determine whether to use a one-sample or two-sample hypothesis test?

**Tip**: In hypothesis testing, always ensure that the null and alternative hypotheses involve the same population parameter (e.g., mean, proportion) with the null typically stating equality and the alternative contradicting it.

For each pair of hypotheses that follows, decide whether H₀ and H₁ are set up correctly as the null and alternative hypotheses for a hypothesis test. If so, select 'Valid' from the drop down menu. If not, select 'Invalid'.
1. H₀: M = 30, H₁: M ≠ 30
2. H₀: μ = 115, H₁: μ ≠ 115
3. H₀: μ = 210, H₁: μ ≠ 210
4. H₀: µ = 130, H₁: µ ≠ 138
You evaluate the null hypothesis by assuming that it is true and testing the reasonableness of this assumption by calculating the probability of getting the results if chance alone is operating.

Understand how to validate null (H₀) and alternative (H₁) hypotheses in hypothesis testing, with examples including means and population parameters. This guide explains key concepts such as two-tailed hypothesis tests and proper setup for statistical inference, suited for undergraduate students.

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