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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. (Round to three decimal places as needed.)

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. (Round to three decimal places as needed.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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**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. [ ] (Round to three decimal places as needed.)
Transcribed Image Text:**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. [ ] (Round to three decimal places as needed.)
**Understanding the t-Distribution Table** The table presents values from the t-distribution, which is used primarily in hypothesis testing and confidence interval estimation for the means of a normally distributed population, especially when the sample size is small and the population standard deviation is unknown. ### Graphical Explanation: - **Bell Curve Diagram**: - Illustrates a symmetric bell-shaped curve, representing the distribution of data. - The shaded area to the right of the curve highlights the "Area in the right tail", which corresponds to the probability significance level (α) for a t-test. ### Table VI: t-Distribution This table provides critical values of the t-distribution for various degrees of freedom (df) and significance levels (identified as the "Area in Right Tail"). #### Columns: - **df (Degrees of Freedom)**: Refers to the number of values in the final calculation of a statistic that are free to vary. It's crucial for determining the specific t-value to use. - **Area in Right Tail**: Indicates different probability levels or significance levels (α = 0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, 0.0005). These are typical alpha levels used in one-tailed tests, indicating the portion of the distribution in the right tail that lies beyond a given t-value. #### Rows: - Each row corresponds to a specific degree of freedom. For instance: - For df = 1, the critical t-value is 1.000 at α = 0.25 and 636.619 at α = 0.0005. - As the degrees of freedom increase, the t-values decrease, reflecting the closer approximation to a normal distribution. #### Interpretation: To find a t-value for a specific degree of freedom and significance level, locate the appropriate row for the degrees of freedom and follow it across to the column of the desired area in the right tail. This t-value can be used in the context of one-sample t-tests, paired sample t-tests, and independent two-sample t-tests. The t-distribution becomes similar to the normal distribution as the degrees of freedom increase. This table is essential for those conducting advanced statistical analyses, especially in the fields of medicine and social sciences, where small
Transcribed Image Text:**Understanding the t-Distribution Table** The table presents values from the t-distribution, which is used primarily in hypothesis testing and confidence interval estimation for the means of a normally distributed population, especially when the sample size is small and the population standard deviation is unknown. ### Graphical Explanation: - **Bell Curve Diagram**: - Illustrates a symmetric bell-shaped curve, representing the distribution of data. - The shaded area to the right of the curve highlights the "Area in the right tail", which corresponds to the probability significance level (α) for a t-test. ### Table VI: t-Distribution This table provides critical values of the t-distribution for various degrees of freedom (df) and significance levels (identified as the "Area in Right Tail"). #### Columns: - **df (Degrees of Freedom)**: Refers to the number of values in the final calculation of a statistic that are free to vary. It's crucial for determining the specific t-value to use. - **Area in Right Tail**: Indicates different probability levels or significance levels (α = 0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, 0.0005). These are typical alpha levels used in one-tailed tests, indicating the portion of the distribution in the right tail that lies beyond a given t-value. #### Rows: - Each row corresponds to a specific degree of freedom. For instance: - For df = 1, the critical t-value is 1.000 at α = 0.25 and 636.619 at α = 0.0005. - As the degrees of freedom increase, the t-values decrease, reflecting the closer approximation to a normal distribution. #### Interpretation: To find a t-value for a specific degree of freedom and significance level, locate the appropriate row for the degrees of freedom and follow it across to the column of the desired area in the right tail. This t-value can be used in the context of one-sample t-tests, paired sample t-tests, and independent two-sample t-tests. The t-distribution becomes similar to the normal distribution as the degrees of freedom increase. This table is essential for those conducting advanced statistical analyses, especially in the fields of medicine and social sciences, where small
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