Three randomly selected households are surveyed. The numbers of people in the households are 1, 2, and 12. Assume that samples of size n=2 are randomly selected with replacement from the population of 1, 2, and 12. Listed below are the nine different samples. Complete parts (a) through (c). 1,1 1,2 1,12 2,1 2,2 2,12 12,1 12,2 12,12 O a. 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 our t Du arrent (Type an integer or a fraction. Use ascending order of the sample variances.) NOV 1 b. Compare the population variance to the mean of the sample variances. Choose the correct answer below. O A. The population variance is equal to the square root of the mean of the sample variances. O B. The population variance is equal to the square of the mean of the sample variances.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question
### Sampling Variance Exercise

This exercise involves the analysis of nine randomly selected samples from a given population of household sizes: 1, 2, and 12. Each sample size is \( n = 2 \), and samples are chosen with replacement. 

**A. Calculate Variances and Summarization of Sampling Distribution:**

1. **Sample Listings:**
   The nine different samples listed are as follows:
   - \(1, 1\)
   - \(1, 2\)
   - \(2, 2\)
   - \(2, 12\)
   - \(1, 12\)
   - \(12, 12\)

2. **Variance Calculation:**
   For each of the nine samples, calculate the variance \( s^2 \).

3. **Probability Distribution:**
   Calculate and summarize the distribution of variances, constructing a table to represent the probability distribution of the distinct variance values. 

**Table Format:**

\[
\begin{array}{c|c}
s^2 & \text{Probability} \\
\hline
\text{(Type an integer or a fraction. Use ascending order of the sample variances.)}
\end{array}
\]

**B. Compare Population Variance to the Mean of Sample Variances:**

Choose the correct statement regarding the relationship between the population variance and the mean of the sample variances:

- **Option A:** The population variance is equal to the square root of the mean of the sample variances.
- **Option B:** The population variance is equal to the square of the mean of the sample variances.

Select the correct answer to complete this comparison.

---

This analysis helps understand the relationship between individual sample variances and the overall population variance, an important concept in inferential statistics.
Transcribed Image Text:### Sampling Variance Exercise This exercise involves the analysis of nine randomly selected samples from a given population of household sizes: 1, 2, and 12. Each sample size is \( n = 2 \), and samples are chosen with replacement. **A. Calculate Variances and Summarization of Sampling Distribution:** 1. **Sample Listings:** The nine different samples listed are as follows: - \(1, 1\) - \(1, 2\) - \(2, 2\) - \(2, 12\) - \(1, 12\) - \(12, 12\) 2. **Variance Calculation:** For each of the nine samples, calculate the variance \( s^2 \). 3. **Probability Distribution:** Calculate and summarize the distribution of variances, constructing a table to represent the probability distribution of the distinct variance values. **Table Format:** \[ \begin{array}{c|c} s^2 & \text{Probability} \\ \hline \text{(Type an integer or a fraction. Use ascending order of the sample variances.)} \end{array} \] **B. Compare Population Variance to the Mean of Sample Variances:** Choose the correct statement regarding the relationship between the population variance and the mean of the sample variances: - **Option A:** The population variance is equal to the square root of the mean of the sample variances. - **Option B:** The population variance is equal to the square of the mean of the sample variances. Select the correct answer to complete this comparison. --- This analysis helps understand the relationship between individual sample variances and the overall population variance, an important concept in inferential statistics.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 4 images

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Means
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
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