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4. Use Table 4 of the Appendix to find t for a 0.95 confidence level when the

4. Use Table 4 of the Appendix to find t for a 0.95 confidence level when the

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 4. Make sure to show work!

# T-Distribution Worksheet ### Questions: 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: This worksheet includes a series of questions designed to enhance understanding and application of the t-distribution in the context of statistical analyses. The questions primarily focus on using a t-distribution table to determine critical values for specific confidence levels and sample sizes. ### Context: - **t-distribution (Student's t-distribution)**: It is used in statistics when the sample size is small and the population standard deviation is unknown. It's a symmetrical distribution like the normal distribution but has heavier tails, meaning it is more prone to producing values that fall far from its mean. ### Key Concepts: 1. **Confidence Level**: The probability that the value of a parameter falls within a specified range of values. For instance, a 0.95 confidence level indicates a 95% chance that the population parameter will fall within the confidence interval. 2. **Sample Size**: The number of observations in a sample. 3. **Degrees of Freedom**: Typically calculated as the sample size minus one (n-1). It influences the shape of the t-distribution. 4. **Symmetry of t-distribution**: The t-distribution is symmetric around zero. 5. **Convergence to Normal Distribution**: As the degrees of freedom increase, the t-distribution approaches the normal distribution (also known as Gaussian distribution). ### Graphs and Diagrams: Although the above text does not include specific graphs or diagrams, when working with t-distributions, it is common to refer
Transcribed Image Text:# T-Distribution Worksheet ### Questions: 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: This worksheet includes a series of questions designed to enhance understanding and application of the t-distribution in the context of statistical analyses. The questions primarily focus on using a t-distribution table to determine critical values for specific confidence levels and sample sizes. ### Context: - **t-distribution (Student's t-distribution)**: It is used in statistics when the sample size is small and the population standard deviation is unknown. It's a symmetrical distribution like the normal distribution but has heavier tails, meaning it is more prone to producing values that fall far from its mean. ### Key Concepts: 1. **Confidence Level**: The probability that the value of a parameter falls within a specified range of values. For instance, a 0.95 confidence level indicates a 95% chance that the population parameter will fall within the confidence interval. 2. **Sample Size**: The number of observations in a sample. 3. **Degrees of Freedom**: Typically calculated as the sample size minus one (n-1). It influences the shape of the t-distribution. 4. **Symmetry of t-distribution**: The t-distribution is symmetric around zero. 5. **Convergence to Normal Distribution**: As the degrees of freedom increase, the t-distribution approaches the normal distribution (also known as Gaussian distribution). ### Graphs and Diagrams: Although the above text does not include specific graphs or diagrams, when working with t-distributions, it is common to refer
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