Answer only. ---### Understanding Simple Random Sampling**Objective:** Learn how to determine the number of possible random samples from a population.**Example Problem:**Simple random sampling uses a sample of size $ n $ from a population of size $ N $ to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of **52** bank accounts, we want to take a random sample of **four** accounts in order to learn about the population. How many different random samples of four accounts are possible?---#### Answering the Problem:**Steps to determine the number of different random samples:**1. Identify the size of the population, $ N $. - In this case, $ N = 52 $ bank accounts. 2. Determine the size of the sample, $ n $. - Here, $ n = 4 $ bank accounts.3. Use the combination formula to find the number of different random samples: \[ \binom{N}{n} = \frac{N!}{n!(N-n)!} \]4. Substitute the values into the formula: \[ \binom{52}{4} = \frac{52!}{4!(52-4)!} = \frac{52!}{4! \cdot 48!} \]5. Calculate the value to get the number of possible samples.**Tools for Assistance:**- Click **Read It** for step-by-step instructions on solving similar problems.- Click **Watch It** for a video explanation.- Click **Master It** to practice additional problems and reinforce understanding.---#### Optional: Show My WorkWhat steps or reasoning did you use? Your work may add bonus points toward your score.You can submit "show my work" an unlimited number of times.---#### Additional Resources:- **My Notes:** Keep track of your progress and notes.- **Ask Your Teacher:** Seek help directly from your instructor.- **Practice Another Version:** Try similar problems to practice and improve your skills.**Uploads:**- You have the option to upload files if needed, with a limit of 10 files maximum.---This educational content is designed to help students understand the concept of simple random sampling and how to apply mathematical formulas to solve sampling problems effectively.---

Given, Population Size (N) = 52 Sample Size (n) = 4

Simple random sampling uses a sample of size n from a population of size N to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of 52 bank accounts, we want to take a random sample of four accounts in order to learn about the population. How many different random samples of four accounts are possible?

Simple random sampling uses a sample of size n from a population of size N to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of 52 bank accounts, we want to take a random sample of four accounts in order to learn about the population. How many different random samples of four accounts are possible?

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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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Answer only.

---

### Understanding Simple Random Sampling

**Objective:** Learn how to determine the number of possible random samples from a population.

**Example Problem:**

Simple random sampling uses a sample of size $ n $ from a population of size $ N $ to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of **52** bank accounts, we want to take a random sample of **four** accounts in order to learn about the population. How many different random samples of four accounts are possible?

---

#### Answering the Problem:

**Steps to determine the number of different random samples:**

1. Identify the size of the population, $ N $.
- In this case, $ N = 52 $ bank accounts.

2. Determine the size of the sample, $ n $.
- Here, $ n = 4 $ bank accounts.

3. Use the combination formula to find the number of different random samples:
\[
\binom{N}{n} = \frac{N!}{n!(N-n)!}
\]

4. Substitute the values into the formula:
\[
\binom{52}{4} = \frac{52!}{4!(52-4)!} = \frac{52!}{4! \cdot 48!}
\]

5. Calculate the value to get the number of possible samples.

**Tools for Assistance:**

- Click **Read It** for step-by-step instructions on solving similar problems.
- Click **Watch It** for a video explanation.
- Click **Master It** to practice additional problems and reinforce understanding.

---

#### Optional: Show My Work

What steps or reasoning did you use? Your work may add bonus points toward your score.

You can submit "show my work" an unlimited number of times.

---

#### Additional Resources:

- **My Notes:** Keep track of your progress and notes.
- **Ask Your Teacher:** Seek help directly from your instructor.
- **Practice Another Version:** Try similar problems to practice and improve your skills.

**Uploads:**
- You have the option to upload files if needed, with a limit of 10 files maximum.

---

This educational content is designed to help students understand the concept of simple random sampling and how to apply mathematical formulas to solve sampling problems effectively.

---

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