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When Y,, Y,..,Y, is a random sample from N(u,0), we learned in class that the Y – Į statistic T = S/ п-1 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 T² can be written as the ratio of two independent x random variables, each divided by their respective degrees of freedom. What is, therefore, the distribution of T?

When Y,, Y,..,Y, is a random sample from N(u,0), we learned in class that the Y – Į statistic T = S/ п-1 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 T² can be written as the ratio of two independent x random variables, each divided by their respective degrees of freedom. What is, therefore, the distribution of T?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 14PPS
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When Y,,Y,,.,Y, is a random sample from N(u,0), we learned in class that the Y - u has t distribution with n-1 degrees of freedom, where Y and S are S n-1 statistic T = the sample mean and sample standard deviation, respectively. Write out the form of T? and show algebraically that T2 can be written as the ratio of two independent x² random variables, each divided by their respective degrees of freedom. What is, therefore, the distribution of T?
Transcribed Image Text:When Y,,Y,,.,Y, is a random sample from N(u,0), we learned in class that the Y - u has t distribution with n-1 degrees of freedom, where Y and S are S n-1 statistic T = the sample mean and sample standard deviation, respectively. Write out the form of T? and show algebraically that T2 can be written as the ratio of two independent x² random variables, each divided by their respective degrees of freedom. What is, therefore, the distribution of T?
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