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A 1 – a confidence interval for 0 is ( µ,Ôu), where: P(ô, so s ôu) = 1- a Identify in this expression: the upper confidence bound; - the lower confidence bound; - the estimand; and - the confidence coefficient. What is a pivot? Define the term and give an example. jid

A 1 – a confidence interval for 0 is ( µ,Ôu), where: P(ô, so s ôu) = 1- a Identify in this expression: the upper confidence bound; - the lower confidence bound; - the estimand; and - the confidence coefficient. What is a pivot? Define the term and give an example. jid

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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A 1 – α confidence interval for θ is \( (\hat{\theta}_L, \hat{\theta}_U) \), where: \[ P \left( \hat{\theta}_L \leq \theta \leq \hat{\theta}_U \right) = 1 - \alpha \] Identify in this expression: - the upper confidence bound; - the lower confidence bound; - the estimand; and - the confidence coefficient. --- **What is a pivot?** Define the term and give an example. --- Let \( Y_1, \ldots, Y_n \overset{iid}{\sim} f(y; \mu) \) where \( \mu = E Y_i \). Write the formulae for: - a large-sample interval for \( \mu \); - a small-sample interval for \( \mu \). --- Let \( Y_1, \ldots, Y_n \overset{iid}{\sim} f(y; \mu_y) \) where \( \mu_y = E Y_i \) and \( X_1, \ldots, X_m \overset{iid}{\sim} g(x; \mu_x) \) where \( \mu_x = E X_i \) be independent random samples. Write the formula for: - a confidence interval for \( \mu_x - \mu_y \) when the variances are equal; - a confidence interval for \( \mu_x - \mu_y \) when the variances are not equal.
Transcribed Image Text:A 1 – α confidence interval for θ is \( (\hat{\theta}_L, \hat{\theta}_U) \), where: \[ P \left( \hat{\theta}_L \leq \theta \leq \hat{\theta}_U \right) = 1 - \alpha \] Identify in this expression: - the upper confidence bound; - the lower confidence bound; - the estimand; and - the confidence coefficient. --- **What is a pivot?** Define the term and give an example. --- Let \( Y_1, \ldots, Y_n \overset{iid}{\sim} f(y; \mu) \) where \( \mu = E Y_i \). Write the formulae for: - a large-sample interval for \( \mu \); - a small-sample interval for \( \mu \). --- Let \( Y_1, \ldots, Y_n \overset{iid}{\sim} f(y; \mu_y) \) where \( \mu_y = E Y_i \) and \( X_1, \ldots, X_m \overset{iid}{\sim} g(x; \mu_x) \) where \( \mu_x = E X_i \) be independent random samples. Write the formula for: - a confidence interval for \( \mu_x - \mu_y \) when the variances are equal; - a confidence interval for \( \mu_x - \mu_y \) when the variances are not equal.
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