Probabilities (Upper Tail) for the t DistributionConceptual Overview: This graph is a utility for finding critical values for the t distribution.NOTE: This graph can be used instead of a standard table of t values found in a textbook.Use the slider to select the df, the degrees of freedom. Then drag the area of the upper tail to select the desired probability for the tail area.The left boundary edge the upper tail area is the critical value and corresponds to the entries in a standard table of t-values. 1. At $ df = 14 $, what is the critical t-value for a lower-tail probability of 0.05? - a. -1.761 - b. 1.708 - c. -1.697 - d. 1.676 - Select (dropdown menu)2. A statistical procedure returned a test statistic of $ t = 0.833 $, $ df = 27 $. What is the upper-tail $ p $-value for the test statistic? - a. 0.833 - b. 0.206 - c. 0.211 - d. 0.794 - Select (dropdown menu) The image displays a chi-squared distribution graph with 2 degrees of freedom (df = 2). - **Graph Explanation:** - The x-axis ranges from -6 to 6, indicating the range of chi-squared values. - The peak of the curve is centered near zero, which is a characteristic of chi-squared distributions with low degrees of freedom. - The shaded area under the curve to the right of x = 2.92 represents the critical region for a significance level of p = 0.05. This shaded region indicates where values would be considered statistically significant in a right-tailed test. - The degree of freedom, displayed as df = 2, can be adjusted along a scale ranging from 0 to 100, showing it is a variable parameter.This visualization helps in understanding the significance threshold and how the distribution behaves with different degrees of freedom.

1. Critical value: Here, the degrees of freedom for the test is 14. The critical value is -1.761 using the excel formula “=T.INV(0.05,14)”. Correct answer is option (a). The graph is shown below.2. P-value: It is given that the test statistic value is 0.833 and the df is 27. The right tailed P-value for the t-test is 0.206 which can be obtained using the excel formula, “=T.DIST.RT (0.833,27)”. Correct answer is option (b). The graph is shown below.

Answered: 1. At df = 14, what is the critical…

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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Conceptual Overview: This graph is a utility for finding critical values for the t distribution.

NOTE: This graph can be used instead of a standard table of t values found in a textbook.

Use the slider to select the df, the degrees of freedom. Then drag the area of the upper tail to select the desired probability for the tail area.

The left boundary edge the upper tail area is the critical value and corresponds to the entries in a standard table of t-values.

1. At $ df = 14 $, what is the critical t-value for a lower-tail probability of 0.05?
- a. -1.761
- b. 1.708
- c. -1.697
- d. 1.676
- Select (dropdown menu)

2. A statistical procedure returned a test statistic of $ t = 0.833 $, $ df = 27 $. What is the upper-tail $ p $-value for the test statistic?
- a. 0.833
- b. 0.206
- c. 0.211
- d. 0.794
- Select (dropdown menu)

The image displays a chi-squared distribution graph with 2 degrees of freedom (df = 2).

- **Graph Explanation:**
- The x-axis ranges from -6 to 6, indicating the range of chi-squared values.
- The peak of the curve is centered near zero, which is a characteristic of chi-squared distributions with low degrees of freedom.
- The shaded area under the curve to the right of x = 2.92 represents the critical region for a significance level of p = 0.05. This shaded region indicates where values would be considered statistically significant in a right-tailed test.
- The degree of freedom, displayed as df = 2, can be adjusted along a scale ranging from 0 to 100, showing it is a variable parameter.

This visualization helps in understanding the significance threshold and how the distribution behaves with different degrees of freedom.

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