3. This question requires you to work z score problems with the sampling distribution of means. For each problem, begin by computing the standard error of the mean, using the formula: Then make two diagrams of the problem-one in terms of the actual scores, and one in terms of the z scores; mark the area under investigation on each curve. Show calculation of the appropriate z scores. List the line(s) from the z score table that you use to answer the question. Provide a verbal answer to each question. a. Assume you have a sampling distribution of means of samples of size n=16 from a population distribution in which u = 46 and o = 36. What proportion of sample means fall above M = 48? b. Assume you have a sampling distribution of means of samples of size n=25 from a population distribution in which u = 100 and o = 15. What proportion of sample means fall above M = 96? c. Assume you have a sampling distribution of means of samples of size n=49 from a population distribution in which u = 44 and o = 14. What proportion of sample means fall below M = 47?
3. This question requires you to work z score problems with the sampling distribution of means. For each problem, begin by computing the standard error of the mean, using the formula: Then make two diagrams of the problem-one in terms of the actual scores, and one in terms of the z scores; mark the area under investigation on each curve. Show calculation of the appropriate z scores. List the line(s) from the z score table that you use to answer the question. Provide a verbal answer to each question. a. Assume you have a sampling distribution of means of samples of size n=16 from a population distribution in which u = 46 and o = 36. What proportion of sample means fall above M = 48? b. Assume you have a sampling distribution of means of samples of size n=25 from a population distribution in which u = 100 and o = 15. What proportion of sample means fall above M = 96? c. Assume you have a sampling distribution of means of samples of size n=49 from a population distribution in which u = 44 and o = 14. What proportion of sample means fall below M = 47?
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
![Certainly! Here's the transcription for educational purposes:
---
8. **This question requires you to work z score problems with the sampling distribution of means.** For each problem, begin by computing the standard error of the mean, using the formula:
\[
\sigma_M = \frac{\sigma}{\sqrt{n}}
\]
Then make two diagrams of the problem—one in terms of the actual scores, and one in terms of the z scores; mark the area under investigation on each curve. Show calculation of the appropriate z scores. List the line(s) from the z score table that you use to answer the question. Provide a verbal answer to each question.
a. Assume you have a sampling distribution of means of samples of size \( n = 16 \) from a population distribution in which \( \mu = 46 \) and \( \sigma = 36 \). What proportion of sample means fall above \( M = 48 \)?
b. Assume you have a sampling distribution of means of samples of size \( n = 25 \) from a population distribution in which \( \mu = 100 \) and \( \sigma = 15 \). What proportion of sample means fall above \( M = 96 \)?
c. Assume you have a sampling distribution of means of samples of size \( n = 49 \) from a population distribution in which \( \mu = 44 \) and \( \sigma = 14 \). What proportion of sample means fall below \( M = 47 \)?
---
**Instructions for the Graphs/Diagrams:**
1. **Diagram 1: Actual Scores**
- Plot a normal distribution curve representing the population distribution.
- Indicate the mean (\(\mu\)) on the horizontal axis.
- Mark the sample mean (\(M\)) on the curve.
- Shade the area that corresponds to the probability question being asked.
2. **Diagram 2: Z Scores**
- Convert the actual score problem into z scores using the formula for z scores.
- Plot a standard normal distribution curve.
- Mark and shade the appropriate areas on this curve to visually represent the probability of z scores.
Ensure to annotate and label key points on the graphs, such as the mean (\(\mu\)), standard deviation (\(\sigma\)), sample mean (M), and the corresponding z scores.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce1f5b4b-8383-4046-aac1-79f29edf7ea2%2Ff7ae31ff-a8fc-4156-a9c8-a7448f791378%2Fm5kkymd_processed.png&w=3840&q=75)
Transcribed Image Text:Certainly! Here's the transcription for educational purposes:
---
8. **This question requires you to work z score problems with the sampling distribution of means.** For each problem, begin by computing the standard error of the mean, using the formula:
\[
\sigma_M = \frac{\sigma}{\sqrt{n}}
\]
Then make two diagrams of the problem—one in terms of the actual scores, and one in terms of the z scores; mark the area under investigation on each curve. Show calculation of the appropriate z scores. List the line(s) from the z score table that you use to answer the question. Provide a verbal answer to each question.
a. Assume you have a sampling distribution of means of samples of size \( n = 16 \) from a population distribution in which \( \mu = 46 \) and \( \sigma = 36 \). What proportion of sample means fall above \( M = 48 \)?
b. Assume you have a sampling distribution of means of samples of size \( n = 25 \) from a population distribution in which \( \mu = 100 \) and \( \sigma = 15 \). What proportion of sample means fall above \( M = 96 \)?
c. Assume you have a sampling distribution of means of samples of size \( n = 49 \) from a population distribution in which \( \mu = 44 \) and \( \sigma = 14 \). What proportion of sample means fall below \( M = 47 \)?
---
**Instructions for the Graphs/Diagrams:**
1. **Diagram 1: Actual Scores**
- Plot a normal distribution curve representing the population distribution.
- Indicate the mean (\(\mu\)) on the horizontal axis.
- Mark the sample mean (\(M\)) on the curve.
- Shade the area that corresponds to the probability question being asked.
2. **Diagram 2: Z Scores**
- Convert the actual score problem into z scores using the formula for z scores.
- Plot a standard normal distribution curve.
- Mark and shade the appropriate areas on this curve to visually represent the probability of z scores.
Ensure to annotate and label key points on the graphs, such as the mean (\(\mu\)), standard deviation (\(\sigma\)), sample mean (M), and the corresponding z scores.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman