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5. When Y,.Y,..Y, is a random sample from N(4,0), we learned in class that the Y-u has 1 distribution with n-1 degrees of freedom, where Y and S are statistic T = - the sample mean and sample standard deviation, respectively. Write out the form of T and show algebraically that T can be written as the ratio of two independent z* random variables, each divided by their respective degrees of freedom. What is, therefore, the distribution of T? (5 pts.)

5. When Y,.Y,..Y, is a random sample from N(4,0), we learned in class that the Y-u has 1 distribution with n-1 degrees of freedom, where Y and S are statistic T = - the sample mean and sample standard deviation, respectively. Write out the form of T and show algebraically that T can be written as the ratio of two independent z* random variables, each divided by their respective degrees of freedom. What is, therefore, the distribution of T? (5 pts.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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5. When Y,,Y,..,Y, is a random sample from N(u,0). we learned in class that the Y-u statistic T = has t distribution with n-1 degrees of freedom, where Y and S are the sample mean and sample standard deviation, respectively. Write out the form of T² and show algebraically that T can be written as the ratio of two independent z random variables, each divided by their respective degrees of freedom. What is, therefore, the distribution of T? (5 pts.)
Transcribed Image Text:5. When Y,,Y,..,Y, is a random sample from N(u,0). we learned in class that the Y-u statistic T = has t distribution with n-1 degrees of freedom, where Y and S are the sample mean and sample standard deviation, respectively. Write out the form of T² and show algebraically that T can be written as the ratio of two independent z random variables, each divided by their respective degrees of freedom. What is, therefore, the distribution of T? (5 pts.)
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