A population consists of the following 6 values: {10, 20, 30, 40, 50, 60}. A sample of size 3 will be chosen from this population without replacement and the median of the sample will be computed: { (0.5 (£n/2 + £n/2+1) m = x(n+1)/2 n odd n even In other words, in a sample of size n = 3 ordered from smallest to largest the median is the 2nd number. The median of a discrete random variable, μ, is defined as the value of such that and P(X M) ≤ 0.5 Determine the median of the population. Think of the population as an equally likely sample space. Determine the sampling distribution of the sample median, m for this population by (1) identifying all possible samples (how many are there?), (2) calculating the median in each sample and (3) using that to determine the probability of each median. Calculate E (m) Determine the standard error or the sample median
A population consists of the following 6 values: {10, 20, 30, 40, 50, 60}. A sample of size 3 will be chosen from this population without replacement and the median of the sample will be computed: { (0.5 (£n/2 + £n/2+1) m = x(n+1)/2 n odd n even In other words, in a sample of size n = 3 ordered from smallest to largest the median is the 2nd number. The median of a discrete random variable, μ, is defined as the value of such that and P(X M) ≤ 0.5 Determine the median of the population. Think of the population as an equally likely sample space. Determine the sampling distribution of the sample median, m for this population by (1) identifying all possible samples (how many are there?), (2) calculating the median in each sample and (3) using that to determine the probability of each median. Calculate E (m) Determine the standard error or the sample median
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
![A population consists of the following 6 values: {10, 20, 30, 40, 50, 60}. A sample of size 3 will be chosen from this population without replacement and the median of the sample will be computed:
\[
m =
\begin{cases}
x_{(n+1)/2} & \text{n odd} \\
0.5 \left(x_{n/2} + x_{n/2+1}\right) & \text{n even}
\end{cases}
\]
In other words, in a sample of size \(n = 3\) ordered from smallest to largest the median is the 2nd number.
The median of a discrete random variable, \(\tilde{\mu}\), is defined as the value of \(\tilde{\mu}\) such that
\[
P(X < \tilde{\mu}) \leq 0.5 \quad \text{and} \quad P(X > \tilde{\mu}) \leq 0.5
\]
Determine the median of the population. Think of the population as an equally likely sample space.
1. **Determine the sampling distribution of the sample median**, \(m\) for this population by:
- Identifying all possible samples (how many are there?),
- Calculating the median in each sample, and
- Using that to determine the probability of each median.
2. **Calculate \(E(m)\)**
3. Determine the standard error or the sample median.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1941a39f-dbc9-477a-8528-f1bffe3dd4bc%2Fcf894431-7b13-4b10-93ce-177573c2a7df%2Fb0yml4_processed.png&w=3840&q=75)
Transcribed Image Text:A population consists of the following 6 values: {10, 20, 30, 40, 50, 60}. A sample of size 3 will be chosen from this population without replacement and the median of the sample will be computed:
\[
m =
\begin{cases}
x_{(n+1)/2} & \text{n odd} \\
0.5 \left(x_{n/2} + x_{n/2+1}\right) & \text{n even}
\end{cases}
\]
In other words, in a sample of size \(n = 3\) ordered from smallest to largest the median is the 2nd number.
The median of a discrete random variable, \(\tilde{\mu}\), is defined as the value of \(\tilde{\mu}\) such that
\[
P(X < \tilde{\mu}) \leq 0.5 \quad \text{and} \quad P(X > \tilde{\mu}) \leq 0.5
\]
Determine the median of the population. Think of the population as an equally likely sample space.
1. **Determine the sampling distribution of the sample median**, \(m\) for this population by:
- Identifying all possible samples (how many are there?),
- Calculating the median in each sample, and
- Using that to determine the probability of each median.
2. **Calculate \(E(m)\)**
3. Determine the standard error or the sample median.
Expert Solution
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 4 steps
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