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You may need to use the appropriate appendix table or technology to answer this question. Find the t value(s) for each of the following cases. (Round your answers to three decimal places.) (a) upper tail area of 0.025 with 12 degrees of freedom 2.179 (b) lower tail area of 0.05 with 52 degrees of freedom -1.676 (c) upper tail area of 0.01 with 30 degrees of freedom -2.458 (d) where 90% of the area falls between these two t values with 29 degrees of freedom and both t values are the same distance from 0 smaller value larger value (e) where 95% of the area falls between these two t values with 45 degrees of freedom and both t values are the same distance from 0 smaller value larger value Need Help? Read It Master It

You may need to use the appropriate appendix table or technology to answer this question. Find the t value(s) for each of the following cases. (Round your answers to three decimal places.) (a) upper tail area of 0.025 with 12 degrees of freedom 2.179 (b) lower tail area of 0.05 with 52 degrees of freedom -1.676 (c) upper tail area of 0.01 with 30 degrees of freedom -2.458 (d) where 90% of the area falls between these two t values with 29 degrees of freedom and both t values are the same distance from 0 smaller value larger value (e) where 95% of the area falls between these two t values with 45 degrees of freedom and both t values are the same distance from 0 smaller value larger value Need Help? Read It Master It

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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# T-Value Calculations and Interpretations In this exercise, we are tasked with finding specific t values and intervals based on given degrees of freedom (df) and tail areas. Below are the required t values and the method to derive them: ### (a) Upper Tail Area Calculation **Condition:** Upper tail area of 0.025 with 12 degrees of freedom **Result:** \[ t = 2.179 \] ### (b) Lower Tail Area Calculation **Condition:** Lower tail area of 0.05 with 52 degrees of freedom **Result:** \[ t = -1.676 \] ### (c) Upper Tail Area Calculation **Condition:** Upper tail area of 0.01 with 30 degrees of freedom **Result:** \[ t = 2.458 \] ### (d) 90% Confidence Interval **Condition:** 90% of the area falls between these two t values with 29 degrees of freedom and both t values are the same distance from 0 **Smaller Value:** (Input required) **Larger Value:** (Input required) ### (e) 95% Confidence Interval **Condition:** 95% of the area falls between these two t values with 45 degrees of freedom and both t values are the same distance from 0 **Smaller Value:** (Input required) **Larger Value:** (Input required) For parts (d) and (e), you would generally use a t-distribution table or statistical software to find the exact values by ensuring 90% or 95% of the area respectively falls between these critical values. ### Helpful Resources - **Read It:** Comprehensive resources to understand t-distribution and related calculations. - **Master It:** Interactive tool for mastering statistical concepts and calculations. Remember to round your final t values to three decimal places for accuracy. --- This page is designed to help students and educators understand the process of finding and interpreting t values from statistical data sets. Such knowledge is fundamental in hypothesis testing and confidence interval estimation in statistics.
Transcribed Image Text:# T-Value Calculations and Interpretations In this exercise, we are tasked with finding specific t values and intervals based on given degrees of freedom (df) and tail areas. Below are the required t values and the method to derive them: ### (a) Upper Tail Area Calculation **Condition:** Upper tail area of 0.025 with 12 degrees of freedom **Result:** \[ t = 2.179 \] ### (b) Lower Tail Area Calculation **Condition:** Lower tail area of 0.05 with 52 degrees of freedom **Result:** \[ t = -1.676 \] ### (c) Upper Tail Area Calculation **Condition:** Upper tail area of 0.01 with 30 degrees of freedom **Result:** \[ t = 2.458 \] ### (d) 90% Confidence Interval **Condition:** 90% of the area falls between these two t values with 29 degrees of freedom and both t values are the same distance from 0 **Smaller Value:** (Input required) **Larger Value:** (Input required) ### (e) 95% Confidence Interval **Condition:** 95% of the area falls between these two t values with 45 degrees of freedom and both t values are the same distance from 0 **Smaller Value:** (Input required) **Larger Value:** (Input required) For parts (d) and (e), you would generally use a t-distribution table or statistical software to find the exact values by ensuring 90% or 95% of the area respectively falls between these critical values. ### Helpful Resources - **Read It:** Comprehensive resources to understand t-distribution and related calculations. - **Master It:** Interactive tool for mastering statistical concepts and calculations. Remember to round your final t values to three decimal places for accuracy. --- This page is designed to help students and educators understand the process of finding and interpreting t values from statistical data sets. Such knowledge is fundamental in hypothesis testing and confidence interval estimation in statistics.
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