Homework Help is Here – Start Your Trial Now!
Math
Statistics
Determine whether the statement below makes sense or does not make sense. Explain clearly.

Determine whether the statement below makes sense or does not make sense. Explain clearly.

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
### Understanding Confidence Intervals #### Explanation Determine whether the statement below makes sense or does not make sense. Explain clearly. **Statement:** Based on our sample, the 95% confidence interval for the mean amount of television watched by adults in a nation is 2.9 to 4.3 hours per day. Therefore, there is a 95% chance that the mean for all adults in the nation will fall somewhere in this range and a 5% chance that it will not. --- #### Multiple Choice Question Choose the correct answer below. **A.** The statement makes sense. There is a 5% probability that the confidence interval limits do not contain the true value of the sample mean, so the probability it does not contain the true value of the population mean is also 5%. **B.** The statement does not make sense. The population mean is a fixed constant that either falls within the confidence interval or it does not. There is no probability associated with this. **C.** The statement does not make sense. The probability the population mean is greater than the upper limit is 5% and the probability it is less than the lower limit is 5%, so the probability it does not is 5% + 5% = 10%. **D.** The statement makes sense. There is 95% probability that the confidence interval limits actually contain the true value of the population mean, so the probability it does not fall in this range is 100% − 95% = 5%. --- #### Analysis A confidence interval, in this context, gives a range derived from sample data within which we are *95% certain* that the true population mean lies. This does not imply a probabilistic measure as applicable to the truth of mean if viewed as fixed but rather on the method’s efficacy over repeated sampling. **Correct Answer:** **B.** The statement does not make sense. The population mean is a fixed constant that either falls within the confidence interval or it does not. There is no probability associated with this. Understanding confidence intervals is crucial in statistics, signifying through numerous samples, 95% will contain the true population mean, underpinning methodological reliability without assigning probability to specific interval outcomes.
Transcribed Image Text:### Understanding Confidence Intervals #### Explanation Determine whether the statement below makes sense or does not make sense. Explain clearly. **Statement:** Based on our sample, the 95% confidence interval for the mean amount of television watched by adults in a nation is 2.9 to 4.3 hours per day. Therefore, there is a 95% chance that the mean for all adults in the nation will fall somewhere in this range and a 5% chance that it will not. --- #### Multiple Choice Question Choose the correct answer below. **A.** The statement makes sense. There is a 5% probability that the confidence interval limits do not contain the true value of the sample mean, so the probability it does not contain the true value of the population mean is also 5%. **B.** The statement does not make sense. The population mean is a fixed constant that either falls within the confidence interval or it does not. There is no probability associated with this. **C.** The statement does not make sense. The probability the population mean is greater than the upper limit is 5% and the probability it is less than the lower limit is 5%, so the probability it does not is 5% + 5% = 10%. **D.** The statement makes sense. There is 95% probability that the confidence interval limits actually contain the true value of the population mean, so the probability it does not fall in this range is 100% − 95% = 5%. --- #### Analysis A confidence interval, in this context, gives a range derived from sample data within which we are *95% certain* that the true population mean lies. This does not imply a probabilistic measure as applicable to the truth of mean if viewed as fixed but rather on the method’s efficacy over repeated sampling. **Correct Answer:** **B.** The statement does not make sense. The population mean is a fixed constant that either falls within the confidence interval or it does not. There is no probability associated with this. Understanding confidence intervals is crucial in statistics, signifying through numerous samples, 95% will contain the true population mean, underpinning methodological reliability without assigning probability to specific interval outcomes.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

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