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2. Statistical Literacy To test for an x distribution that is mound-shaped us- ing sample size n ≥ 30, how do you decide whether to use the normal or the Student's t distribution?

2. Statistical Literacy To test for an x distribution that is mound-shaped us- ing sample size n ≥ 30, how do you decide whether to use the normal or the Student's t distribution?

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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Please answer number 2. Make sure to show work! Thanks!
### Statistical Literacy and Critical Thinking in Hypothesis Testing #### 2. Statistical Literacy To test \(\mu\) for an \(x\) distribution that is mound-shaped using sample size \(n \geq 30\), how do you decide whether to use the normal or the Student’s \(t\) distribution? #### 3. Statistical Literacy When using the Student’s \(t\) distribution to test \(\mu\), what value do you use for the degrees of freedom? #### 4. Critical Thinking Consider a test for \(\mu\). If the \(P\)-value is such that you can reject \(H_0\) at the 5% level of significance, can you always reject \(H_0\) at the 1% level of significance? Explain. #### 5. Critical Thinking Consider a test for \(\mu\). If the \(P\)-value is such that you can reject \(H_0\) for \(\alpha = 0.01\), can you always reject \(H_0\) for \(\alpha = 0.05\)? Explain. #### 6. Critical Thinking If sample data is such that for a one-tailed test of \(\mu\) you can reject \(H_0\) at the 1% level of significance, can you always reject \(H_0\) for a two-tailed test at the same level of significance? Explain. #### 7. Basic Computation: P-value Corresponding to t Value For a Student’s \(t\) distribution with \(d.f. = 10\) and \(t = 2.930\): (a) Find an interval containing the corresponding \(P\)-value for a two-tailed test. (b) Find an interval containing the corresponding \(P\)-value for a right-tailed test. --- This content covers key concepts in hypothesis testing, including the use of the Student's \(t\) distribution, critical thinking about \(P\)-values, and how to determine appropriate degrees of freedom. Understanding these concepts is crucial for accurate statistical analysis and interpretation.
Transcribed Image Text:### Statistical Literacy and Critical Thinking in Hypothesis Testing #### 2. Statistical Literacy To test \(\mu\) for an \(x\) distribution that is mound-shaped using sample size \(n \geq 30\), how do you decide whether to use the normal or the Student’s \(t\) distribution? #### 3. Statistical Literacy When using the Student’s \(t\) distribution to test \(\mu\), what value do you use for the degrees of freedom? #### 4. Critical Thinking Consider a test for \(\mu\). If the \(P\)-value is such that you can reject \(H_0\) at the 5% level of significance, can you always reject \(H_0\) at the 1% level of significance? Explain. #### 5. Critical Thinking Consider a test for \(\mu\). If the \(P\)-value is such that you can reject \(H_0\) for \(\alpha = 0.01\), can you always reject \(H_0\) for \(\alpha = 0.05\)? Explain. #### 6. Critical Thinking If sample data is such that for a one-tailed test of \(\mu\) you can reject \(H_0\) at the 1% level of significance, can you always reject \(H_0\) for a two-tailed test at the same level of significance? Explain. #### 7. Basic Computation: P-value Corresponding to t Value For a Student’s \(t\) distribution with \(d.f. = 10\) and \(t = 2.930\): (a) Find an interval containing the corresponding \(P\)-value for a two-tailed test. (b) Find an interval containing the corresponding \(P\)-value for a right-tailed test. --- This content covers key concepts in hypothesis testing, including the use of the Student's \(t\) distribution, critical thinking about \(P\)-values, and how to determine appropriate degrees of freedom. Understanding these concepts is crucial for accurate statistical analysis and interpretation.
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