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Find the critical value(s) and rejection region(s) for the indicated t-test, level of significance a, and sample size n. Two-tailed test, a=0.02, n 16 Click the icon to view the t-distribution table. ...*. The critical value(s) is/are (Round to the nearest thousandh as needed. Use a comma to separate answers as needed.)

Find the critical value(s) and rejection region(s) for the indicated t-test, level of significance a, and sample size n. Two-tailed test, a=0.02, n 16 Click the icon to view the t-distribution table. ...*. The critical value(s) is/are (Round to the nearest thousandh as needed. Use a comma to separate answers as needed.)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Find the critical value and rejection region
**Transcription for Educational Website:** --- **Finding Critical Values for a T-Test** To find the critical value(s) and rejection region(s) for a t-test: - **Two-tailed test**, significance level \(\alpha = 0.02\), sample size \(n = 16\). **Steps:** 1. Determine the degrees of freedom (d.f.) using the formula \(d.f. = n - 1\). 2. Click the icon to view the t-distribution table. **Critical Value(s) Calculation:** - The critical value(s) is/are \(___ \) (Round to the nearest thousandth as needed. Use a comma to separate multiple answers.) **T-Distribution Table:** - The table displays critical values for various levels of confidence \(c\). | **Level of confidence, \(c\)** | **0.80** | **0.90** | **0.95** | **0.98** | **0.99** | |----------------------------------|----------|----------|----------|----------|----------| | **One tail, \(\alpha\)** | **0.10** | **0.05** | **0.025**| **0.01** | **0.005**| | **Two tails, \(\alpha\)** | | **0.10** | **0.05** | **0.02** | **0.01** | The degrees of freedom (d.f.) are displayed vertically. For each \(d.f.\), find the corresponding critical value intersecting with the desired confidence level column. - Example for \(d.f. = 16\): - 0.80 Confidence Level: 1.337 - 0.90 Confidence Level: 1.746 - 0.95 Confidence Level: 2.120 - 0.98 Confidence Level: 2.583 - 0.99 Confidence Level: 2.921 **Navigation Buttons:** - **Print**: Print the table. - **Done**: Exit the table view. **Help Options:** - **Help me solve this**: Assistance for solving the problem. - **View an example**: See an example problem. - **Get more help**: Access additional resources. --- This transcription provides
Transcribed Image Text:**Transcription for Educational Website:** --- **Finding Critical Values for a T-Test** To find the critical value(s) and rejection region(s) for a t-test: - **Two-tailed test**, significance level \(\alpha = 0.02\), sample size \(n = 16\). **Steps:** 1. Determine the degrees of freedom (d.f.) using the formula \(d.f. = n - 1\). 2. Click the icon to view the t-distribution table. **Critical Value(s) Calculation:** - The critical value(s) is/are \(___ \) (Round to the nearest thousandth as needed. Use a comma to separate multiple answers.) **T-Distribution Table:** - The table displays critical values for various levels of confidence \(c\). | **Level of confidence, \(c\)** | **0.80** | **0.90** | **0.95** | **0.98** | **0.99** | |----------------------------------|----------|----------|----------|----------|----------| | **One tail, \(\alpha\)** | **0.10** | **0.05** | **0.025**| **0.01** | **0.005**| | **Two tails, \(\alpha\)** | | **0.10** | **0.05** | **0.02** | **0.01** | The degrees of freedom (d.f.) are displayed vertically. For each \(d.f.\), find the corresponding critical value intersecting with the desired confidence level column. - Example for \(d.f. = 16\): - 0.80 Confidence Level: 1.337 - 0.90 Confidence Level: 1.746 - 0.95 Confidence Level: 2.120 - 0.98 Confidence Level: 2.583 - 0.99 Confidence Level: 2.921 **Navigation Buttons:** - **Print**: Print the table. - **Done**: Exit the table view. **Help Options:** - **Help me solve this**: Assistance for solving the problem. - **View an example**: See an example problem. - **Get more help**: Access additional resources. --- This transcription provides
**Finding Critical Values and Rejection Regions for a Two-Tailed T-Test** To perform a two-tailed t-test, you need to identify the critical value(s) and the rejection region(s) based on the given level of significance \(\alpha\) and sample size \(n\). **Parameters Given:** - **Level of Significance (\(\alpha\))**: 0.02 - **Sample Size (n)**: 16 ### Steps: 1. **Access the t-Distribution Table:** - Click the provided icon to view the t-distribution table. 2. **Determine the Critical Value(s):** - Find the critical value(s) by locating the degrees of freedom (\(df = n - 1\)) and the given \(\alpha\) in the t-distribution table. - Since this is a two-tailed test, divide the \(\alpha\) value by 2 to find the critical value for each tail. - For \(n = 16\), the degrees of freedom (df) will be 15. - Use the values found to determine the critical t-values on the t-distribution table at \(\alpha/2 = 0.01\). 3. **Critical Value Input:** - Enter the critical value(s) in the provided box. - Remember to round the critical t-value(s) to the nearest thousandth and separate multiple values with a comma if needed. ### Additional Resources: - **Help Options:** - "Help me solve this" for step-by-step guidance. - "View an example" to see a similar problem solved. - "Get more help" for further assistance. By understanding these steps, you'll be able to determine the rejection regions for your hypothesis test using the t-distribution.
Transcribed Image Text:**Finding Critical Values and Rejection Regions for a Two-Tailed T-Test** To perform a two-tailed t-test, you need to identify the critical value(s) and the rejection region(s) based on the given level of significance \(\alpha\) and sample size \(n\). **Parameters Given:** - **Level of Significance (\(\alpha\))**: 0.02 - **Sample Size (n)**: 16 ### Steps: 1. **Access the t-Distribution Table:** - Click the provided icon to view the t-distribution table. 2. **Determine the Critical Value(s):** - Find the critical value(s) by locating the degrees of freedom (\(df = n - 1\)) and the given \(\alpha\) in the t-distribution table. - Since this is a two-tailed test, divide the \(\alpha\) value by 2 to find the critical value for each tail. - For \(n = 16\), the degrees of freedom (df) will be 15. - Use the values found to determine the critical t-values on the t-distribution table at \(\alpha/2 = 0.01\). 3. **Critical Value Input:** - Enter the critical value(s) in the provided box. - Remember to round the critical t-value(s) to the nearest thousandth and separate multiple values with a comma if needed. ### Additional Resources: - **Help Options:** - "Help me solve this" for step-by-step guidance. - "View an example" to see a similar problem solved. - "Get more help" for further assistance. By understanding these steps, you'll be able to determine the rejection regions for your hypothesis test using the t-distribution.
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