How do I solve this? ### 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 DiagramsThere 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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Description: How do I solve this? ### 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 nei

Identify the type of test used to find the critical value to construct the confidence interval. The…

Math

Statistics

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

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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

How do I solve this?

### 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

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