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
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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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.
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![### 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
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### 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. \( t_{\alpha / 2} = 2.602 \)
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