Question #1 Part B **Understanding the t-Distribution Table**This document presents a t-distribution table for critical values of t at various levels of significance for one-tailed tests. The table is often used in statistical analyses involving small sample sizes or when the population standard deviation is unknown. Below the table is a quick reference for statistical analysis using a t-distribution.### Graph ExplanationIn the top left corner, there's a graph depicting a t-distribution curve. The graph shows a bell-shaped curve where a shaded area representing the "Area in right tail" is highlighted. This area corresponds to the tails referenced in significance testing, indicating the probability of a value falling in the extreme right end of the distribution.### Table Structure**Table VI: t-Distribution - Area in Right Tail**The table lists critical t-values according to degrees of freedom (df) and significance levels (alpha). These levels range from 0.25 to 0.0005.- **df (Degrees of Freedom)**: Listed vertically on the left side, from 1 to 80.- **Significance Levels (Alpha)**: Enumerated horizontally across the top, showing 0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, and 0.0005.### How to Use This TableTo find a critical t-value:1. Select your desired level of significance (alpha) from the top row.2. Identify your degrees of freedom (df) in the first column.3. Locate the intersection point of your df row and alpha column to determine the critical t-value for your test.### ExampleSuppose you have 10 degrees of freedom and are conducting a test at the 0.05 significance level. According to this table:- Find df = 10 in the first column.- Move horizontally across to the 0.05 column.- The critical t-value is **1.812**. Use these values to interpret statistical tests and decide about hypotheses concerning sample data relative to the t-distribution. Determine the t-value in each of the cases.Click the icon to view the table of areas under the t-distribution.---(a) Find the t-value such that the area in the right tail is 0.05 with 11 degrees of freedom.- 1.796 (Round to three decimal places as needed.)(b) Find the t-value such that the area in the right tail is 0.005 with 7 degrees of freedom.- [ ] (Round to three decimal places as needed.)

The t value at significance level = 0.005 And degree of freedom is 7 The t value for right tailed is by standard table of t 3.499

Math

Statistics

-Area in right tail Table VI t-Distribution Area in Right Tail df 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 1.376 1.061 0.978 0.941 1.963 1.386 1.250 1.190 1.156 3.078 6.314 12.706 4.303 3.182 2.776 2.571 15.894 4.849 3.482 2.999 31.821 6.965 4.541 3.747 63.657 9.925 127.321 14.089 7.453 5.598 4.773 318.309 22.327 636.619 31.599 12.924 8.610 1.000 0.816 0.765 0.741 0.727 1.886 2.920 2.353 1.638 1.533 2.132 1.476 2.015 5.841 10.215 4.604 7.173 0.920 2.757 3.365 4.032 5.893 6.869 3.707 3.499 2.447 2.365 2.306 2.262 2.228 4.317 4.029 3.833 3.690 3.581 5.208 4.785 4.501 4.297 5.959 5.408 5.041 4.781 4.587 0.718 0.711 0.906 0.896 0.889 0.883 1.134 1.119 1.440 1.415 1.943 1.895 1.860 1.383 1.833 1.812 2.612 2.517 2.449 2.398 2.359 3.143 2.998 7 0.706 1.108 1.397 2.896 3.355 9 0.703 2.821 1.100 1.093 3.250 3.169 10 0.700 0.879 1.372 2.764 4.144 11 12 0.876 0.873 1.363 1.356 1.796 1.782 2.328 2.303 2.718 2.681 3.106 3.055 3.497 3.428 1 277 0.697 1.088 2.201 4.025 4.437 0.695 1.083 2.179 3.930 4.318 13 0 604 0870 1.070 1250 1.771 1160 2282 2650 2012 2952 1221 1234 56

-Area in right tail Table VI t-Distribution Area in Right Tail df 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 1.376 1.061 0.978 0.941 1.963 1.386 1.250 1.190 1.156 3.078 6.314 12.706 4.303 3.182 2.776 2.571 15.894 4.849 3.482 2.999 31.821 6.965 4.541 3.747 63.657 9.925 127.321 14.089 7.453 5.598 4.773 318.309 22.327 636.619 31.599 12.924 8.610 1.000 0.816 0.765 0.741 0.727 1.886 2.920 2.353 1.638 1.533 2.132 1.476 2.015 5.841 10.215 4.604 7.173 0.920 2.757 3.365 4.032 5.893 6.869 3.707 3.499 2.447 2.365 2.306 2.262 2.228 4.317 4.029 3.833 3.690 3.581 5.208 4.785 4.501 4.297 5.959 5.408 5.041 4.781 4.587 0.718 0.711 0.906 0.896 0.889 0.883 1.134 1.119 1.440 1.415 1.943 1.895 1.860 1.383 1.833 1.812 2.612 2.517 2.449 2.398 2.359 3.143 2.998 7 0.706 1.108 1.397 2.896 3.355 9 0.703 2.821 1.100 1.093 3.250 3.169 10 0.700 0.879 1.372 2.764 4.144 11 12 0.876 0.873 1.363 1.356 1.796 1.782 2.328 2.303 2.718 2.681 3.106 3.055 3.497 3.428 1 277 0.697 1.088 2.201 4.025 4.437 0.695 1.083 2.179 3.930 4.318 13 0 604 0870 1.070 1250 1.771 1160 2282 2650 2012 2952 1221 1234 56

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

Question #1 Part B

**Understanding the t-Distribution Table**

This document presents a t-distribution table for critical values of t at various levels of significance for one-tailed tests. The table is often used in statistical analyses involving small sample sizes or when the population standard deviation is unknown. Below the table is a quick reference for statistical analysis using a t-distribution.

### Graph Explanation

In the top left corner, there's a graph depicting a t-distribution curve. The graph shows a bell-shaped curve where a shaded area representing the "Area in right tail" is highlighted. This area corresponds to the tails referenced in significance testing, indicating the probability of a value falling in the extreme right end of the distribution.

### Table Structure

**Table VI: t-Distribution - Area in Right Tail**

The table lists critical t-values according to degrees of freedom (df) and significance levels (alpha). These levels range from 0.25 to 0.0005.

- **df (Degrees of Freedom)**: Listed vertically on the left side, from 1 to 80.
- **Significance Levels (Alpha)**: Enumerated horizontally across the top, showing 0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, and 0.0005.

### How to Use This Table

To find a critical t-value:
1. Select your desired level of significance (alpha) from the top row.
2. Identify your degrees of freedom (df) in the first column.
3. Locate the intersection point of your df row and alpha column to determine the critical t-value for your test.

### Example

Suppose you have 10 degrees of freedom and are conducting a test at the 0.05 significance level. According to this table:
- Find df = 10 in the first column.
- Move horizontally across to the 0.05 column.
- The critical t-value is **1.812**.

Use these values to interpret statistical tests and decide about hypotheses concerning sample data relative to the t-distribution.

Determine the t-value in each of the cases.

Click the icon to view the table of areas under the t-distribution.

---

(a) Find the t-value such that the area in the right tail is 0.05 with 11 degrees of freedom.

- 1.796 (Round to three decimal places as needed.)

(b) Find the t-value such that the area in the right tail is 0.005 with 7 degrees of freedom.

- [ ] (Round to three decimal places as needed.)

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