Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of o=9. We have taken a random sample of size n-60 from the population. This is Sample 1 in the table below. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.) As shown in the table, the sample mean of Sample 1 is x = 81.1. Also shown are the lower and upper limits of the 75% confidence interval for the population mean using this sample, as well as the lower and upper limits of the 95% confidence interval. Suppose that the true mean of the population is μ = 80, which is shown on the displays for the confidence intervals. Press the "Generate Samples" button to simulate taking 19 more random samples of size n=60 from this same population. (The 75% and 95% confidence intervals for all of the samples are shown in the table and graphed.) Then complete parts (a) through (c) below the table.
Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of o=9. We have taken a random sample of size n-60 from the population. This is Sample 1 in the table below. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.) As shown in the table, the sample mean of Sample 1 is x = 81.1. Also shown are the lower and upper limits of the 75% confidence interval for the population mean using this sample, as well as the lower and upper limits of the 95% confidence interval. Suppose that the true mean of the population is μ = 80, which is shown on the displays for the confidence intervals. Press the "Generate Samples" button to simulate taking 19 more random samples of size n=60 from this same population. (The 75% and 95% confidence intervals for all of the samples are shown in the table and graphed.) Then complete parts (a) through (c) below the table.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of o=9. We have taken a
random sample of size n = 60 from the population. This is Sample 1 in the table below. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.) As
shown in the table, the sample mean of Sample 1 is x = 81.1. Also shown are the lower and upper limits of the 75% confidence interval for the population mean
using this sample, as well as the lower and upper limits of the 95% confidence interval. Suppose that the true mean of the population is μ = 80, which is shown
on the displays for the confidence intervals.
Press the "Generate Samples" button to simulate taking 19 more random samples of size n = 60 from this same population. (The 75% and 95% confidence
intervals for all of the samples are shown in the table and graphed.) Then complete parts (a) through (c) below the table.
75% 75% 95% 95%
lower upper lower
limit
limit limit
upper
limit
S1 81.1 79.8
82.4 78.8 83.4
S2 80.8 79.5 82.1 78.5 83.1
S3 80.1 78.8 81.4 77.8
82.4
80.6 77.0 81.6
S4 79.3 78.0
S5 81.0 79.7
82.3 78.7 83.3
S6 81.8 80.5
83.1 79.5 84.1
S7 80.2
78.9
81.5 77.9 82.5
82.8
S8 80.5 79.2
81.8
78.2
S9 78.3 77.0 79.6
76.0 80.6
510 78.1 76.8 79.4 75.8
80.4
81.0 77.4
82.0
81.1 77.5 82.1
S11 79.7 78.4
S12 79.8 78.5
S13 80.8 79.5
S14 80.9 79.6
82.1 78.5 83.1
82.2 78.6 83.2
82.9
S15 80.6 79.3
81.9 78.3
S16 79.7 78.4 81.0 77.4 82.0
S17 82.6 81.3
83.9
80.3 84.9
S18 79.8
78.5
81.1 77.5 82.1
S19 79.1
77.8 80.4
76.8
81.4
S20 80.1 78.8 81.4 77.8 82.4
X
75.0
75% confidence intervals
85.0 75.0
95% confidence intervals
85.0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c10e8ad-3433-42a7-ad9a-20db80d2b0e4%2Fe27444ce-c9bb-4f0c-a0df-0a120676d923%2F115mxib_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of o=9. We have taken a
random sample of size n = 60 from the population. This is Sample 1 in the table below. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.) As
shown in the table, the sample mean of Sample 1 is x = 81.1. Also shown are the lower and upper limits of the 75% confidence interval for the population mean
using this sample, as well as the lower and upper limits of the 95% confidence interval. Suppose that the true mean of the population is μ = 80, which is shown
on the displays for the confidence intervals.
Press the "Generate Samples" button to simulate taking 19 more random samples of size n = 60 from this same population. (The 75% and 95% confidence
intervals for all of the samples are shown in the table and graphed.) Then complete parts (a) through (c) below the table.
75% 75% 95% 95%
lower upper lower
limit
limit limit
upper
limit
S1 81.1 79.8
82.4 78.8 83.4
S2 80.8 79.5 82.1 78.5 83.1
S3 80.1 78.8 81.4 77.8
82.4
80.6 77.0 81.6
S4 79.3 78.0
S5 81.0 79.7
82.3 78.7 83.3
S6 81.8 80.5
83.1 79.5 84.1
S7 80.2
78.9
81.5 77.9 82.5
82.8
S8 80.5 79.2
81.8
78.2
S9 78.3 77.0 79.6
76.0 80.6
510 78.1 76.8 79.4 75.8
80.4
81.0 77.4
82.0
81.1 77.5 82.1
S11 79.7 78.4
S12 79.8 78.5
S13 80.8 79.5
S14 80.9 79.6
82.1 78.5 83.1
82.2 78.6 83.2
82.9
S15 80.6 79.3
81.9 78.3
S16 79.7 78.4 81.0 77.4 82.0
S17 82.6 81.3
83.9
80.3 84.9
S18 79.8
78.5
81.1 77.5 82.1
S19 79.1
77.8 80.4
76.8
81.4
S20 80.1 78.8 81.4 77.8 82.4
X
75.0
75% confidence intervals
85.0 75.0
95% confidence intervals
85.0
![(a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, μ = 80?
(b) How many of the 95% confidence intervals constructed from the 20 samples contain the population mean, μ = 80?
(c) Choose ALL that are true.
It is not surprising that some 75% confidence intervals are different from other 75% confidence intervals. Each
confidence interval depends on its sample, and different samples may give different confidence intervals.
O All of the 95% confidence intervals should be the same as each other. Since they are not all the same, there must
have been errors due to rounding.
The center of the 75% confidence interval for Sample 1 is 80, because the center of any confidence interval for the
population mean must be the population mean.
We would expect to find more 75% confidence intervals that contain the population mean than 95% confidence
intervals that contain the population mean. Given a sample, a higher confidence level results in a narrower interval.
None of the choices above are true.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c10e8ad-3433-42a7-ad9a-20db80d2b0e4%2Fe27444ce-c9bb-4f0c-a0df-0a120676d923%2Fqnzvipe_processed.png&w=3840&q=75)
Transcribed Image Text:(a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, μ = 80?
(b) How many of the 95% confidence intervals constructed from the 20 samples contain the population mean, μ = 80?
(c) Choose ALL that are true.
It is not surprising that some 75% confidence intervals are different from other 75% confidence intervals. Each
confidence interval depends on its sample, and different samples may give different confidence intervals.
O All of the 95% confidence intervals should be the same as each other. Since they are not all the same, there must
have been errors due to rounding.
The center of the 75% confidence interval for Sample 1 is 80, because the center of any confidence interval for the
population mean must be the population mean.
We would expect to find more 75% confidence intervals that contain the population mean than 95% confidence
intervals that contain the population mean. Given a sample, a higher confidence level results in a narrower interval.
None of the choices above are true.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
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](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman