Fill in the blanks to correctly complete the sentence below. Suppose a simple random sample of size n is drawn from a large population with mean u and standard deviation o. The sampling distribution of x has mean u- and standa Suppose a simple random sample of size n is drawn from a large population with mean u and standard deviation o. The sampling distribution of x has mean u- = V and standan
Fill in the blanks to correctly complete the sentence below. Suppose a simple random sample of size n is drawn from a large population with mean u and standard deviation o. The sampling distribution of x has mean u- and standa Suppose a simple random sample of size n is drawn from a large population with mean u and standard deviation o. The sampling distribution of x has mean u- = V and standan
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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Question
14-
![Fill in the blanks to correctly complete the sentence below.
Suppose a simple random sample of size \( n \) is drawn from a large population with mean \( \mu \) and standard deviation \( \sigma \). The sampling distribution of \( \bar{x} \) has mean \( \mu_{\bar{x}} = \) [fill in the blank] and standard deviation \( \sigma_{\bar{x}} = \) [fill in the blank].
---
Suppose a simple random sample of size \( n \) is drawn from a large population with mean \( \mu \) and standard deviation \( \sigma \). The sampling distribution of \( \bar{x} \) has mean \( \mu_{\bar{x}} = \) [dropdown option] and standard deviation \( \sigma_{\bar{x}} = \) [dropdown menu with options]:
- \(\frac{\sigma}{\sqrt{n}}\)
- \(\frac{\mu}{n}\)
- \(\mu\)
- \(\frac{\mu}{\sqrt{n}}\)
- \(\frac{\sigma}{n}\)
- \(\sigma\)
Time Remaining: [Timer Icon]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F314336d9-9cd2-4a69-ac2b-dc8a3c81cf54%2Fc6e3a065-4952-42c0-8cc0-df0c74cf3150%2F9ajvdv_processed.png&w=3840&q=75)
Transcribed Image Text:Fill in the blanks to correctly complete the sentence below.
Suppose a simple random sample of size \( n \) is drawn from a large population with mean \( \mu \) and standard deviation \( \sigma \). The sampling distribution of \( \bar{x} \) has mean \( \mu_{\bar{x}} = \) [fill in the blank] and standard deviation \( \sigma_{\bar{x}} = \) [fill in the blank].
---
Suppose a simple random sample of size \( n \) is drawn from a large population with mean \( \mu \) and standard deviation \( \sigma \). The sampling distribution of \( \bar{x} \) has mean \( \mu_{\bar{x}} = \) [dropdown option] and standard deviation \( \sigma_{\bar{x}} = \) [dropdown menu with options]:
- \(\frac{\sigma}{\sqrt{n}}\)
- \(\frac{\mu}{n}\)
- \(\mu\)
- \(\frac{\mu}{\sqrt{n}}\)
- \(\frac{\sigma}{n}\)
- \(\sigma\)
Time Remaining: [Timer Icon]
![**Educational Content: Understanding Sampling Distributions**
---
**Interactive Practice: Completing the Sentence**
In this exercise, you are tasked with understanding key concepts about sampling distributions. Fill in the blanks to correctly complete the sentence.
Suppose a simple random sample of size \( n \) is drawn from a large population with mean \( \mu \) and standard deviation \( \sigma \). The sampling distribution of \( \overline{x} \) has:
- **Mean** \( \mu_{\overline{x}} = \) [Dropdown menu]
- **Standard Deviation** \( \sigma_{\overline{x}} = \) [Dropdown menu]
---
**Dropdown Options:**
1. \( \sigma \)
2. \( \sqrt{n} \)
3. \( \sigma \)
4. \( \mu \)
5. \( \frac{\mu}{\sqrt{n}} \)
---
**Solution Explanation:**
When dealing with a simple random sample taken from a larger population:
- The mean of the sampling distribution \( \mu_{\overline{x}} \) is equal to the population mean, \( \mu \).
- The standard deviation of the sampling distribution \( \sigma_{\overline{x}} \), often referred to as the standard error, is \( \frac{\sigma}{\sqrt{n}} \), where \( \sigma \) is the population standard deviation and \( n \) is the sample size.
Understanding these concepts is crucial for statistical inference and helps describe how sample means vary around the population mean.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F314336d9-9cd2-4a69-ac2b-dc8a3c81cf54%2Fc6e3a065-4952-42c0-8cc0-df0c74cf3150%2Fdqcbiv_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Content: Understanding Sampling Distributions**
---
**Interactive Practice: Completing the Sentence**
In this exercise, you are tasked with understanding key concepts about sampling distributions. Fill in the blanks to correctly complete the sentence.
Suppose a simple random sample of size \( n \) is drawn from a large population with mean \( \mu \) and standard deviation \( \sigma \). The sampling distribution of \( \overline{x} \) has:
- **Mean** \( \mu_{\overline{x}} = \) [Dropdown menu]
- **Standard Deviation** \( \sigma_{\overline{x}} = \) [Dropdown menu]
---
**Dropdown Options:**
1. \( \sigma \)
2. \( \sqrt{n} \)
3. \( \sigma \)
4. \( \mu \)
5. \( \frac{\mu}{\sqrt{n}} \)
---
**Solution Explanation:**
When dealing with a simple random sample taken from a larger population:
- The mean of the sampling distribution \( \mu_{\overline{x}} \) is equal to the population mean, \( \mu \).
- The standard deviation of the sampling distribution \( \sigma_{\overline{x}} \), often referred to as the standard error, is \( \frac{\sigma}{\sqrt{n}} \), where \( \sigma \) is the population standard deviation and \( n \) is the sample size.
Understanding these concepts is crucial for statistical inference and helps describe how sample means vary around the population mean.
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