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6. Statistical Literacy As the degrees of freedom increase, what distribution does the Student's t distribution become more like?

6. Statistical Literacy As the degrees of freedom increase, what distribution does the Student's t distribution become more like?

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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Please answer number 6. Make sure to show work! Thanks!

### Problems 1. **Use Table 4 of the Appendix to find \( t_c \) for a 0.95 confidence level when the sample size is 18.** 2. **Use Table 4 of the Appendix to find \( t_c \) for a 0.99 confidence level when the sample size is 4.** 3. **Use Table 4 of the Appendix to find \( t_c \) for a 0.90 confidence level when the sample size is 22.** 4. **Use Table 4 of the Appendix to find \( t_c \) for a 0.95 confidence level when the sample size is 12.** 5. **Statistical Literacy**: Student’s *t* distributions are symmetric about a value of \( t \). What is that \( t \) value? 6. **Statistical Literacy**: As the degrees of freedom increase, what distribution does the Student’s *t* distribution become more like? ### Explanation of Tables and Distributions - **Table 4 of the Appendix**: This table typically provides critical values of the Student's t-distribution for different confidence levels and degrees of freedom. These values are used to calculate confidence intervals and perform hypothesis testing. - **Symmetry in t Distributions**: The Student's t-distribution is symmetric about zero. Thus, the value of \( t \) in question 5 is generally 0. - **Degrees of Freedom and Distribution Convergence**: As the degrees of freedom increase, the Student’s t-distribution approaches a normal distribution. This means that at higher degrees of freedom, the shape of the t-distribution becomes more like the familiar bell curve of the normal distribution. This is key for understanding statistical methods in larger sample sizes. Understanding how to use these values and their implications are crucial for statistical computations and inferential statistics. Make sure to refer to the specific table in your appendix for the precise critical values needed in each problem.
Transcribed Image Text:### Problems 1. **Use Table 4 of the Appendix to find \( t_c \) for a 0.95 confidence level when the sample size is 18.** 2. **Use Table 4 of the Appendix to find \( t_c \) for a 0.99 confidence level when the sample size is 4.** 3. **Use Table 4 of the Appendix to find \( t_c \) for a 0.90 confidence level when the sample size is 22.** 4. **Use Table 4 of the Appendix to find \( t_c \) for a 0.95 confidence level when the sample size is 12.** 5. **Statistical Literacy**: Student’s *t* distributions are symmetric about a value of \( t \). What is that \( t \) value? 6. **Statistical Literacy**: As the degrees of freedom increase, what distribution does the Student’s *t* distribution become more like? ### Explanation of Tables and Distributions - **Table 4 of the Appendix**: This table typically provides critical values of the Student's t-distribution for different confidence levels and degrees of freedom. These values are used to calculate confidence intervals and perform hypothesis testing. - **Symmetry in t Distributions**: The Student's t-distribution is symmetric about zero. Thus, the value of \( t \) in question 5 is generally 0. - **Degrees of Freedom and Distribution Convergence**: As the degrees of freedom increase, the Student’s t-distribution approaches a normal distribution. This means that at higher degrees of freedom, the shape of the t-distribution becomes more like the familiar bell curve of the normal distribution. This is key for understanding statistical methods in larger sample sizes. Understanding how to use these values and their implications are crucial for statistical computations and inferential statistics. Make sure to refer to the specific table in your appendix for the precise critical values needed in each problem.
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