Find the critical value to for the confidence level c = 0.90 and sample size n = 21. t₁ = Click the icon to view the t-distribution table. (Round to the nearest thousandth as needed.) t-Distribution Table d.f. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Level of confidence, c One tail, a Two tails, a 0.99 0.005 0.80 0.90 0.95 0.98 0.10 0.05 0.025 0.01 0.20 0.10 0.05 0.02 3.078 6.314 12.706 31.821 1.886 2.920 4.303 6.965 1.638 2.353 3.182 4.541 1.533 2.132 2.776 3.747 0.01 d.f. 63.657 9.925 5.841 4.604 4.032 3.707 1.476 2.015 2.571 3.365 3.143 1.440 1.943 2.447 1.415 1.895 2.365 2.998 3.499 1.397 1.860 2.306 2.896 3.355 1.383 1.833 2.262 1.372 1.812 2.228 1.363 1.796 2.201 1.356 1.782 2.179 1.350 1.771 2.160 2.821 3.250 2.764 3.169 2.718 3.106 2.681 3.055 3.012 2.977 2.650 1.345 1.761 2.145 2.624 1.341 1.337 1.746 2.120 1.333 1.740 2.110 1.330 1.734 2.101 1.328 1.729 2.093 1.325 1.725 2.086 2.528 1.753 2.131 2.602 2.947 2.583 2.921 2.567 2.898 2.552 2.878 2.539 2.861 2.845 1.323 1.721 2.080 2.518 2.831 1.321 1.717 2.074 2.508 2.819 1.319 1.714 2.069 2.500 2.807 2.797 1.318 1.711 2.064 2.492 1.316 1.708 2.060 2.485 2.787 712 3 THELBGONHARDANNERH 10 12 15 16 17 18 19 20 21 23 24 - D
Find the critical value to for the confidence level c = 0.90 and sample size n = 21. t₁ = Click the icon to view the t-distribution table. (Round to the nearest thousandth as needed.) t-Distribution Table d.f. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Level of confidence, c One tail, a Two tails, a 0.99 0.005 0.80 0.90 0.95 0.98 0.10 0.05 0.025 0.01 0.20 0.10 0.05 0.02 3.078 6.314 12.706 31.821 1.886 2.920 4.303 6.965 1.638 2.353 3.182 4.541 1.533 2.132 2.776 3.747 0.01 d.f. 63.657 9.925 5.841 4.604 4.032 3.707 1.476 2.015 2.571 3.365 3.143 1.440 1.943 2.447 1.415 1.895 2.365 2.998 3.499 1.397 1.860 2.306 2.896 3.355 1.383 1.833 2.262 1.372 1.812 2.228 1.363 1.796 2.201 1.356 1.782 2.179 1.350 1.771 2.160 2.821 3.250 2.764 3.169 2.718 3.106 2.681 3.055 3.012 2.977 2.650 1.345 1.761 2.145 2.624 1.341 1.337 1.746 2.120 1.333 1.740 2.110 1.330 1.734 2.101 1.328 1.729 2.093 1.325 1.725 2.086 2.528 1.753 2.131 2.602 2.947 2.583 2.921 2.567 2.898 2.552 2.878 2.539 2.861 2.845 1.323 1.721 2.080 2.518 2.831 1.321 1.717 2.074 2.508 2.819 1.319 1.714 2.069 2.500 2.807 2.797 1.318 1.711 2.064 2.492 1.316 1.708 2.060 2.485 2.787 712 3 THELBGONHARDANNERH 10 12 15 16 17 18 19 20 21 23 24 - D
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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![**Finding the Critical Value \( t_c \) for Confidence Level \( c = 0.90 \) and Sample Size \( n = 21 \)**
To calculate the critical value \( t_c \), use the t-distribution table provided.
**Steps to Follow:**
1. **Identify the Degrees of Freedom (d.f.):**
- The degrees of freedom (d.f.) is calculated as the sample size minus one. For a sample size \( n = 21 \):
\[
\text{d.f.} = n - 1 = 21 - 1 = 20
\]
2. **Locate the Confidence Level Column:**
- Use the t-distribution table and find the column for the confidence level \( c = 0.90 \). This corresponds to "Two tails, \( \alpha = 0.10 \)."
3. **Find the Critical Value:**
- With \( \text{d.f.} = 20 \) and \( \alpha = 0.10 \), locate the intersection of the correct row and column.
- The critical value \( t_c \) is 1.325.
4. **Round as Needed:**
- Round \( t_c \) to the nearest thousandth as instructed.
**t-Distribution Table Overview:**
- The table lists degrees of freedom (d.f.) from 1 to 25 on the far left column.
- It includes columns corresponding to different confidence levels and tail probabilities (\( \alpha \)).
- Each cell in the table provides the critical value of \( t \) for the given d.f. and confidence level.
This information is essential for conducting hypothesis tests and creating confidence intervals in statistics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38aa5034-1eec-4964-a430-19a44c4ef4d5%2F63d65328-3573-4616-9103-9cc5cd801f7f%2Fk3lkxl_processed.png&w=3840&q=75)
Transcribed Image Text:**Finding the Critical Value \( t_c \) for Confidence Level \( c = 0.90 \) and Sample Size \( n = 21 \)**
To calculate the critical value \( t_c \), use the t-distribution table provided.
**Steps to Follow:**
1. **Identify the Degrees of Freedom (d.f.):**
- The degrees of freedom (d.f.) is calculated as the sample size minus one. For a sample size \( n = 21 \):
\[
\text{d.f.} = n - 1 = 21 - 1 = 20
\]
2. **Locate the Confidence Level Column:**
- Use the t-distribution table and find the column for the confidence level \( c = 0.90 \). This corresponds to "Two tails, \( \alpha = 0.10 \)."
3. **Find the Critical Value:**
- With \( \text{d.f.} = 20 \) and \( \alpha = 0.10 \), locate the intersection of the correct row and column.
- The critical value \( t_c \) is 1.325.
4. **Round as Needed:**
- Round \( t_c \) to the nearest thousandth as instructed.
**t-Distribution Table Overview:**
- The table lists degrees of freedom (d.f.) from 1 to 25 on the far left column.
- It includes columns corresponding to different confidence levels and tail probabilities (\( \alpha \)).
- Each cell in the table provides the critical value of \( t \) for the given d.f. and confidence level.
This information is essential for conducting hypothesis tests and creating confidence intervals in statistics.
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