Homework Help is Here – Start Your Trial Now!
Math
Statistics
Is the difference between the two indicators significant at the 95% confidence level?

Is the difference between the two indicators significant at the 95% confidence level?

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
See similar textbooks
icon
Related questions
Question
Write clearly so I can see
The image presents a problem regarding concentration measurements of acid using two indicators. **Details:** An analyst measured the concentration of acid in a solution using two different indicators. The results are summarized as follows: - **Mean [HCl] ± Standard Deviation (# measurements):** - Indicator A: 0.02467 ± 0.0045 (18 measurements) - Indicator B: 0.02407 ± 0.0032 (12 measurements) **Question:** Is the difference between the two indicators significant at the 95% confidence level? The problem requires determining if the means of the two sets of measurements are significantly different at a 95% confidence level, which typically involves statistical analysis such as a t-test.
Transcribed Image Text:The image presents a problem regarding concentration measurements of acid using two indicators. **Details:** An analyst measured the concentration of acid in a solution using two different indicators. The results are summarized as follows: - **Mean [HCl] ± Standard Deviation (# measurements):** - Indicator A: 0.02467 ± 0.0045 (18 measurements) - Indicator B: 0.02407 ± 0.0032 (12 measurements) **Question:** Is the difference between the two indicators significant at the 95% confidence level? The problem requires determining if the means of the two sets of measurements are significantly different at a 95% confidence level, which typically involves statistical analysis such as a t-test.
The image displays a section of a t-distribution table, which is used to determine the critical values of the t-distribution based on degrees of freedom and confidence levels. ### Table Breakdown: - **Degrees of Freedom:** This is listed vertically in the first column. It represents the number of independent values that can vary in an analysis without breaking any constraints. - **Confidence Levels:** These are displayed horizontally across the top (50, 90, 95, 98, 99, 99.5, 99.9). They indicate the probability that a given range encompasses the true population parameter. ### Explanation: For each degree of freedom, the corresponding row provides the critical t-values for each specified confidence level. These values are utilized primarily in confidence interval calculations and hypothesis testing where the sample size is small or the population standard deviation is unknown. ### Note: At the bottom, there is a note explaining substitutions in confidence intervals. If a known "true" population standard deviation is determined, 'z' may be used instead of 't'. The value of 't' used in Equation 4-6 is taken from the bottom row of Table #2. This table is essential for students and researchers performing statistical analyses with t-tests, helping them determine critical values for different degrees of freedom and desired confidence levels.
Transcribed Image Text:The image displays a section of a t-distribution table, which is used to determine the critical values of the t-distribution based on degrees of freedom and confidence levels. ### Table Breakdown: - **Degrees of Freedom:** This is listed vertically in the first column. It represents the number of independent values that can vary in an analysis without breaking any constraints. - **Confidence Levels:** These are displayed horizontally across the top (50, 90, 95, 98, 99, 99.5, 99.9). They indicate the probability that a given range encompasses the true population parameter. ### Explanation: For each degree of freedom, the corresponding row provides the critical t-values for each specified confidence level. These values are utilized primarily in confidence interval calculations and hypothesis testing where the sample size is small or the population standard deviation is unknown. ### Note: At the bottom, there is a note explaining substitutions in confidence intervals. If a known "true" population standard deviation is determined, 'z' may be used instead of 't'. The value of 't' used in Equation 4-6 is taken from the bottom row of Table #2. This table is essential for students and researchers performing statistical analyses with t-tests, helping them determine critical values for different degrees of freedom and desired confidence levels.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS