Three randomly selected children are surveyed. The ages of the children are 1, 4, and 10. Assume that samples of size n=2 are randomly selected with replacement from the population of 1, 4, and 10. Listed below are the nine different samples. Complete parts (a) through (d). 1,1 1,4 1,10 4,1 4,4 4,10 10,1 10,4 10,10 a. Find the value of the population variance o². 14 (Round to three decimal places as needed.) b. Find the variance of each of the nine samples, then summarize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values. ▼ ▼ ▼ Probability 26 implified fractions.)
Three randomly selected children are surveyed. The ages of the children are 1, 4, and 10. Assume that samples of size n=2 are randomly selected with replacement from the population of 1, 4, and 10. Listed below are the nine different samples. Complete parts (a) through (d). 1,1 1,4 1,10 4,1 4,4 4,10 10,1 10,4 10,10 a. Find the value of the population variance o². 14 (Round to three decimal places as needed.) b. Find the variance of each of the nine samples, then summarize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values. ▼ ▼ ▼ Probability 26 implified fractions.)
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
![**Title: Understanding Sampling and Variance: A Practical Example**
In this example, we explore concepts of population variance and sampling distribution using a simple scenario involving children's ages.
**Scenario:**
Three randomly selected children are surveyed. The ages of the children are 1, 4, and 10. We assume that samples of size \( n = 2 \) are randomly selected with replacement from this population of ages 1, 4, and 10. The nine different samples are listed below:
- Samples: (1, 1), (1, 4), (1, 10), (4, 1), (4, 4), (4, 10), (10, 1), (10, 4), (10, 10)
**Tasks:**
a. **Population Variance Calculation:**
- Find the value of the population variance (\( \sigma^2 \)).
- Answer: 14 (rounded to three decimal places as needed).
b. **Variance of Each Sample and Sampling Distribution:**
- Calculate the variance of each of the nine samples.
- Construct a table representing the probability distribution of the distinct variance values.
**Probability Distribution Table:**
- The table includes two columns: \( s^2 \) (sample variance) and Probability.
\[
\begin{array}{|c|c|}
\hline
s^2 & \text{Probability} \\
\hline
& \\
& \\
& \\
\hline
\end{array}
\]
- Fill in the sample variances and their corresponding probabilities based on calculated frequencies for each variance.
This exercise aids in understanding the fundamental principles of statistics, focusing on concepts such as population variance and sampling distributions in an educational setting.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F546defb5-634a-4a8e-85bb-5f53f5378fa1%2Fc5709368-65ed-433e-8ad0-e20dbb4f8f22%2Fwnk7o6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Sampling and Variance: A Practical Example**
In this example, we explore concepts of population variance and sampling distribution using a simple scenario involving children's ages.
**Scenario:**
Three randomly selected children are surveyed. The ages of the children are 1, 4, and 10. We assume that samples of size \( n = 2 \) are randomly selected with replacement from this population of ages 1, 4, and 10. The nine different samples are listed below:
- Samples: (1, 1), (1, 4), (1, 10), (4, 1), (4, 4), (4, 10), (10, 1), (10, 4), (10, 10)
**Tasks:**
a. **Population Variance Calculation:**
- Find the value of the population variance (\( \sigma^2 \)).
- Answer: 14 (rounded to three decimal places as needed).
b. **Variance of Each Sample and Sampling Distribution:**
- Calculate the variance of each of the nine samples.
- Construct a table representing the probability distribution of the distinct variance values.
**Probability Distribution Table:**
- The table includes two columns: \( s^2 \) (sample variance) and Probability.
\[
\begin{array}{|c|c|}
\hline
s^2 & \text{Probability} \\
\hline
& \\
& \\
& \\
\hline
\end{array}
\]
- Fill in the sample variances and their corresponding probabilities based on calculated frequencies for each variance.
This exercise aids in understanding the fundamental principles of statistics, focusing on concepts such as population variance and sampling distributions in an educational setting.
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