Do one of the following, as appropriate. (a) Find the critical value z12, (b) find the critical value ty/2, (c) state that neither the normal nor the t distribution applies. Confidence level 98%; n = 16; o is unknown; population appears to be normally distributed. %3D

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### Statistics Problem: Determining Critical Values

**Problem Statement:**
Do one of the following, as appropriate:
(a) Find the critical value \( Z_{\alpha / 2} \).
(b) Find the critical value \( t_{\alpha / 2} \).
(c) State that neither the normal nor the t distribution applies.

Given:
- Confidence level: 98%
- Sample size (\( n \)): 16
- Population standard deviation (\( \sigma \)) is unknown
- Population appears to be normally distributed

**Resources Provided:**
- [Table of Critical t-values](#)
- [Standard Normal Table - Page 1](#)
- [Standard Normal Table - Page 2](#)

**Multiple Choice Options:**

- \( B. \ Z_{\alpha / 2} = 2.055 \)
- \( C. \ t_{\alpha / 2} = 2.602 \)
- \( D. \ t_{\alpha / 2} = 2.249 \)
- \( E. \ Neither normal nor t distribution applies \)

**Action Required:**
Click to select your answer.

---
**Save for Later**
Transcribed Image Text:### Statistics Problem: Determining Critical Values **Problem Statement:** Do one of the following, as appropriate: (a) Find the critical value \( Z_{\alpha / 2} \). (b) Find the critical value \( t_{\alpha / 2} \). (c) State that neither the normal nor the t distribution applies. Given: - Confidence level: 98% - Sample size (\( n \)): 16 - Population standard deviation (\( \sigma \)) is unknown - Population appears to be normally distributed **Resources Provided:** - [Table of Critical t-values](#) - [Standard Normal Table - Page 1](#) - [Standard Normal Table - Page 2](#) **Multiple Choice Options:** - \( B. \ Z_{\alpha / 2} = 2.055 \) - \( C. \ t_{\alpha / 2} = 2.602 \) - \( D. \ t_{\alpha / 2} = 2.249 \) - \( E. \ Neither normal nor t distribution applies \) **Action Required:** Click to select your answer. --- **Save for Later**
### Critical Value Calculation Exercise

**Instructional Task**: 

Do one of the following, as appropriate:
(a) Find the critical value \( z_{\alpha / 2} \).
(b) Find the critical value \( t_{\alpha / 2} \).
(c) State that neither the normal nor the t distribution applies.

**Given**:
- Confidence level: 98%
- Sample size (\( n \)): 16
- Population standard deviation (\( \sigma \)): Unknown
- Population appears to be normally distributed

**Resources**:
- [Click here to view a table of critical t-values.](#)
- [Click here to view page 1 of the standard normal table.](#)
- [Click here to view page 2 of the standard normal table.](#)

**Question**: 

Find the critical value.

**Options**: 
- A. \( z_{\alpha / 2} = 2.33 \)
- B. \( z_{\alpha / 2} = 2.055 \)
- C. \( t_{\alpha / 2} = 2.602 \)

**Answer Selection**:
Click to select your answer.

**Functionality**:
- Save for Later button

---

### Explanation of Graphs and Diagrams

There are no graphs or diagrams present in this exercise. The provided links suggest access to external resources (critical t-values and standard normal tables) which would contain necessary statistical data needed to solve the problem at hand.

### Steps to Solve:
1. **Determine that \(\sigma\) is unknown** and the sample size is small (\( n < 30 \)). Therefore, you typically use the t-distribution, making option (a) irrelevant.
2. **Refer to the t-value table** provided in the link to find the appropriate value for \( t_{\alpha / 2} \) based on degrees of freedom (\( df = n - 1 \)). Here, \( df = 16 - 1 = 15 \).
3. Verify that the t-value for a 98% confidence interval (which corresponds to \( \alpha / 2 = 0.01 \) in each tail) for 15 degrees of freedom matches option (C) \( t_{\alpha / 2} = 2.602 \).

**Answer**: C. \( t_{\alpha / 2} = 2.602 \)

Click
Transcribed Image Text:### Critical Value Calculation Exercise **Instructional Task**: Do one of the following, as appropriate: (a) Find the critical value \( z_{\alpha / 2} \). (b) Find the critical value \( t_{\alpha / 2} \). (c) State that neither the normal nor the t distribution applies. **Given**: - Confidence level: 98% - Sample size (\( n \)): 16 - Population standard deviation (\( \sigma \)): Unknown - Population appears to be normally distributed **Resources**: - [Click here to view a table of critical t-values.](#) - [Click here to view page 1 of the standard normal table.](#) - [Click here to view page 2 of the standard normal table.](#) **Question**: Find the critical value. **Options**: - A. \( z_{\alpha / 2} = 2.33 \) - B. \( z_{\alpha / 2} = 2.055 \) - C. \( t_{\alpha / 2} = 2.602 \) **Answer Selection**: Click to select your answer. **Functionality**: - Save for Later button --- ### Explanation of Graphs and Diagrams There are no graphs or diagrams present in this exercise. The provided links suggest access to external resources (critical t-values and standard normal tables) which would contain necessary statistical data needed to solve the problem at hand. ### Steps to Solve: 1. **Determine that \(\sigma\) is unknown** and the sample size is small (\( n < 30 \)). Therefore, you typically use the t-distribution, making option (a) irrelevant. 2. **Refer to the t-value table** provided in the link to find the appropriate value for \( t_{\alpha / 2} \) based on degrees of freedom (\( df = n - 1 \)). Here, \( df = 16 - 1 = 15 \). 3. Verify that the t-value for a 98% confidence interval (which corresponds to \( \alpha / 2 = 0.01 \) in each tail) for 15 degrees of freedom matches option (C) \( t_{\alpha / 2} = 2.602 \). **Answer**: C. \( t_{\alpha / 2} = 2.602 \) Click
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