### Sampling Variance ExerciseThis 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.

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Description: ### Sampling Variance ExerciseThis 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 Va

a) Sample variances: The following table lists the possible samples with replacement, from the three…

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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.

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

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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.

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