Title: Understanding Sampling Distributions and Population Medians---**Overview:**In this exercise, we are examining the sampling distribution of medians from a small population consisting of the number of people in households: 1, 2, and 12. We are assuming that samples of size $ n = 2 $ are randomly selected with replacement from this population. Here are the different samples: 1,1 ; 1,2 ; 1,12 ; 2,1 ; 2,2 ; 2,12 ; 12,1 ; 12,2 ; 12,12.**Objective:**The goal is to analyze the medians of these samples and understand the relationship between sample medians and the population median.---**Part (a): Sampling Distribution of Sample Medians**Find the median of each of the nine samples, then summarize them into a probability distribution table of distinct median values.**Table:** - Sample Median: List of medians to be calculated. - Probability: Corresponding probability for each sample median.**Instructions:**- Insert integers or fractions.- Use ascending order of sample medians.---**Part (b): Comparison of Population Median and Sample Median Mean**Analyze the relationship between the population median and the mean of the sample medians. Select the correct statement:- **A.** The population median is equal to the mean of the sample medians.- **B.** The population median is equal to double the mean of the sample medians.- **C.** The population median is not equal to the mean of the sample medians (nor half or double).- **D.** The population median is equal to half of the mean of the sample medians.---**Part (c): Evaluation of Sample Medians as Estimators**Examine if sample medians accurately estimate the population median, and evaluate their effectiveness as estimators.- **A.** Sample medians target the population median, making them good estimators.- **B.** Sample medians do not target the population median, yet are good estimators.- **C.** Sample medians do not target the population median, making them poor estimators.- **D.** Sample medians target the population median but are poor estimators.---By understanding the sampling distribution of medians, students will gain insights into how sample statistics relate to population parameters, particularly in the context

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Description: Title: Understanding Sampling Distributions and Population Medians---**Overview:**In this exercise, we are examining the sampling distribution of medians from a small population consisting of the number of people in households: 1, 2, and 12. We are

a. From the given information, Sample Median for each sample 1 1 1 1 2 1.5…

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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 replaceme 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 median of each of the nine samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution of the distinct median values. Sample Median Probability (Type integers or fractions. Use ascending order of the sample medians.) b. Compare the population median to the mean of the sample medians. Choose the correct answer below.

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 replaceme 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 median of each of the nine samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution of the distinct median values. Sample Median Probability (Type integers or fractions. Use ascending order of the sample medians.) b. Compare the population median to the mean of the sample medians. Choose the correct answer below.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Topic Video

Question

Title: Understanding Sampling Distributions and Population Medians

---

**Overview:**

In this exercise, we are examining the sampling distribution of medians from a small population consisting of the number of people in households: 1, 2, and 12. We are assuming that samples of size $ n = 2 $ are randomly selected with replacement from this population. Here are the different samples:
1,1 ; 1,2 ; 1,12 ; 2,1 ; 2,2 ; 2,12 ; 12,1 ; 12,2 ; 12,12.

**Objective:**

The goal is to analyze the medians of these samples and understand the relationship between sample medians and the population median.

---

**Part (a): Sampling Distribution of Sample Medians**

Find the median of each of the nine samples, then summarize them into a probability distribution table of distinct median values.

**Table:**
- Sample Median: List of medians to be calculated.
- Probability: Corresponding probability for each sample median.

**Instructions:**
- Insert integers or fractions.
- Use ascending order of sample medians.

---

**Part (b): Comparison of Population Median and Sample Median Mean**

Analyze the relationship between the population median and the mean of the sample medians. Select the correct statement:

- **A.** The population median is equal to the mean of the sample medians.
- **B.** The population median is equal to double the mean of the sample medians.
- **C.** The population median is not equal to the mean of the sample medians (nor half or double).
- **D.** The population median is equal to half of the mean of the sample medians.

---

**Part (c): Evaluation of Sample Medians as Estimators**

Examine if sample medians accurately estimate the population median, and evaluate their effectiveness as estimators.

- **A.** Sample medians target the population median, making them good estimators.
- **B.** Sample medians do not target the population median, yet are good estimators.
- **C.** Sample medians do not target the population median, making them poor estimators.
- **D.** Sample medians target the population median but are poor estimators.

---

By understanding the sampling distribution of medians, students will gain insights into how sample statistics relate to population parameters, particularly in the context

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