19. Left-tailed test, a = α=0.03

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question 19

### Educational Text on Statistical Testing and Analysis

#### Z-Test Calculation
The image shows two calculator display screens related to a statistical Z-Test. Here's how each part of the process is detailed:

**First Display:**
- **Z-Test:** Shows `Input: Data` and `Stats`.
- **ω (Population mean):** 742
- **σ (Standard deviation):** 68.1
- **x̄ (Sample mean):** 763
- **n (Sample size):** 65
- Test type: Two-tailed (μ ≠ ω)

**Second Display:**
- **ω (Population mean):** 742
- **z (Z-score):** 2.486158777
- **p (P-value):** 0.0064565285
- **x̄ (Sample mean):** 763
- **n (Sample size):** 65

---

#### Finding Critical Values and Rejection Regions

For Exercises 19-24, determine the critical values and rejection regions for z-tests at various levels of significance (α). A graph should accompany your answer.

19. **Left-tailed test, α = 0.03**

20. **Left-tailed test, α = 0.09**

21. **Right-tailed test, α = 0.05**

22. **Right-tailed test, α = 0.08**

23. **Two-tailed test, α = 0.02**

24. **Two-tailed test, α = 0.12**

---

#### Graphical Analysis

For Exercises 25 and 26, determine if the standardized test statistic \( z \) allows rejection of the null hypothesis. Provide reasoning for your decision.

**Exercise 25:**
- (a) \( z = -1.301 \)
- (b) \( z = 1.203 \)
- (c) \( z = 1.280 \)
- (d) \( z = 1.286 \)

**Exercise 26:**
- (a) \( z = 1.98 \)
- (b) \( z = -1.89 \)
- (c) \( z = 1.65 \)
- (d) \( z = -1.99 \)

**Graph Explanation:**
Two bell curve graphs are displayed:
- **Graph for Exercise 25:** A standard normal distribution curve
Transcribed Image Text:### Educational Text on Statistical Testing and Analysis #### Z-Test Calculation The image shows two calculator display screens related to a statistical Z-Test. Here's how each part of the process is detailed: **First Display:** - **Z-Test:** Shows `Input: Data` and `Stats`. - **ω (Population mean):** 742 - **σ (Standard deviation):** 68.1 - **x̄ (Sample mean):** 763 - **n (Sample size):** 65 - Test type: Two-tailed (μ ≠ ω) **Second Display:** - **ω (Population mean):** 742 - **z (Z-score):** 2.486158777 - **p (P-value):** 0.0064565285 - **x̄ (Sample mean):** 763 - **n (Sample size):** 65 --- #### Finding Critical Values and Rejection Regions For Exercises 19-24, determine the critical values and rejection regions for z-tests at various levels of significance (α). A graph should accompany your answer. 19. **Left-tailed test, α = 0.03** 20. **Left-tailed test, α = 0.09** 21. **Right-tailed test, α = 0.05** 22. **Right-tailed test, α = 0.08** 23. **Two-tailed test, α = 0.02** 24. **Two-tailed test, α = 0.12** --- #### Graphical Analysis For Exercises 25 and 26, determine if the standardized test statistic \( z \) allows rejection of the null hypothesis. Provide reasoning for your decision. **Exercise 25:** - (a) \( z = -1.301 \) - (b) \( z = 1.203 \) - (c) \( z = 1.280 \) - (d) \( z = 1.286 \) **Exercise 26:** - (a) \( z = 1.98 \) - (b) \( z = -1.89 \) - (c) \( z = 1.65 \) - (d) \( z = -1.99 \) **Graph Explanation:** Two bell curve graphs are displayed: - **Graph for Exercise 25:** A standard normal distribution curve
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