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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 0.005 with 16 degrees of freedom. (Round to three decimal places as needed.) (b) Find the t-value such that the area in the right tail is 0.02 with 13 degrees of freedom. (Round to three decimal places as needed.) (c) Find the t-value such that the area left of the t-value is 0.025 with 19 degrees of freedom. [Hint: Use symmetry.] (Round to three decimal places as needed.) a Find the eriieel tuelue thet. le te 000

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 0.005 with 16 degrees of freedom. (Round to three decimal places as needed.) (b) Find the t-value such that the area in the right tail is 0.02 with 13 degrees of freedom. (Round to three decimal places as needed.) (c) Find the t-value such that the area left of the t-value is 0.025 with 19 degrees of freedom. [Hint: Use symmetry.] (Round to three decimal places as needed.) a Find the eriieel tuelue thet. le te 000

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
Problem 1P
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**Determine the t-value in each of the cases.**
Transcribed Image Text:**Determine the t-value in each of the cases.**
## Educational Resource: Understanding the t-Distribution Table ### Overview The t-distribution table is an essential tool in statistics, primarily used when conducting hypothesis tests or constructing confidence intervals for small sample sizes. This table helps determine the critical value for the t-distribution based on the desired level of confidence and degrees of freedom (df). ### Diagram Explanation At the top of the image is a bell-shaped curve graph representing the t-distribution. A section of the curve's right tail is highlighted and labeled "Area in right tail." The position of this area is indicated on the horizontal axis with a point labeled "t," signifying the critical value of the t-distribution for the corresponding tail area. ### Table VI: t-Distribution The table is organized into rows and columns. The rows represent various degrees of freedom (df), ranging from 1 to 80. The columns represent the area in the right tail of the distribution and are labeled with different cumulative probabilities: 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 the Table 1. **Identify Degrees of Freedom (df):** Determine the degrees of freedom for your data. This is usually one less than the sample size for a single sample test. 2. **Determine the Desired Tail Area:** Decide the significance level (alpha) or confidence level that you need for your test. For example, for a 95% confidence level, the alpha level is 0.05. 3. **Locate the Critical Value:** Find the intersection of your df row and your desired tail area column. This intersection gives the critical value 't,' which you can use to compare against your test statistic. ### Practical Application This table is most commonly applied in: - **t-tests** (one-sample, two-sample, paired sample) to evaluate hypotheses about population means. - **Confidence interval calculations** for small samples where the standard deviation is unknown and is estimated from the sample. ### Conclusion Mastering the use of the t-distribution table is crucial for tasks involving inference about population means, especially when sample sizes are relatively small. Understanding this tool empowers students and professionals to make informed decisions based on quantitative data analysis.
Transcribed Image Text:## Educational Resource: Understanding the t-Distribution Table ### Overview The t-distribution table is an essential tool in statistics, primarily used when conducting hypothesis tests or constructing confidence intervals for small sample sizes. This table helps determine the critical value for the t-distribution based on the desired level of confidence and degrees of freedom (df). ### Diagram Explanation At the top of the image is a bell-shaped curve graph representing the t-distribution. A section of the curve's right tail is highlighted and labeled "Area in right tail." The position of this area is indicated on the horizontal axis with a point labeled "t," signifying the critical value of the t-distribution for the corresponding tail area. ### Table VI: t-Distribution The table is organized into rows and columns. The rows represent various degrees of freedom (df), ranging from 1 to 80. The columns represent the area in the right tail of the distribution and are labeled with different cumulative probabilities: 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 the Table 1. **Identify Degrees of Freedom (df):** Determine the degrees of freedom for your data. This is usually one less than the sample size for a single sample test. 2. **Determine the Desired Tail Area:** Decide the significance level (alpha) or confidence level that you need for your test. For example, for a 95% confidence level, the alpha level is 0.05. 3. **Locate the Critical Value:** Find the intersection of your df row and your desired tail area column. This intersection gives the critical value 't,' which you can use to compare against your test statistic. ### Practical Application This table is most commonly applied in: - **t-tests** (one-sample, two-sample, paired sample) to evaluate hypotheses about population means. - **Confidence interval calculations** for small samples where the standard deviation is unknown and is estimated from the sample. ### Conclusion Mastering the use of the t-distribution table is crucial for tasks involving inference about population means, especially when sample sizes are relatively small. Understanding this tool empowers students and professionals to make informed decisions based on quantitative data analysis.
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