2. A sample is selected from a population with a mean c. of u = 40 and a standard deviation of o = a. If the sample has n = expected value of M and the standard error of M? b. If the sample has n = expected value of M and the standard error of M? 8. 11. A 4 scores, what is the S possible Dossible 16 scores, what is the mean of
2. A sample is selected from a population with a mean c. of u = 40 and a standard deviation of o = a. If the sample has n = expected value of M and the standard error of M? b. If the sample has n = expected value of M and the standard error of M? 8. 11. A 4 scores, what is the S possible Dossible 16 scores, what is the mean of
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 11MCQ
Related questions
Question
![**Sample Problem for Understanding Statistical Concepts**
Consider the problem below, which involves calculating the expected value and standard error of the mean (M) from a sample drawn from a population:
**Problem Statement:**
A sample is selected from a population with a mean (\(\mu\)) of 40 and a standard deviation (\(\sigma\)) of 8.
a. If the sample has \(n = 4\) scores, what is the expected value of \(M\) and the standard error of \(M\)?
b. If the sample has \(n = 16\) scores, what is the expected value of \(M\) and the standard error of \(M\)?
**Explanation:**
To solve this problem, we will use the following statistical concepts:
1. **Expected Value of \(M\):** This is equal to the population mean (\(\mu\)). Since the expected value measures the central location of the distribution of the sample mean, it remains the same as the population mean regardless of the sample size.
2. **Standard Error of \(M\):** This is calculated using the formula:
\[
\text{Standard Error of } M = \frac{\sigma}{\sqrt{n}}
\]
where \(\sigma\) is the standard deviation of the population, and \(n\) is the sample size. The standard error measures the variability of the sample mean around the population mean. It decreases as the sample size increases.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcfc3ce54-1f7c-4ae6-b3e7-6da4bbb533d5%2F7e1ccecf-cb04-4465-8905-347816465914%2Fbd49v47_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Sample Problem for Understanding Statistical Concepts**
Consider the problem below, which involves calculating the expected value and standard error of the mean (M) from a sample drawn from a population:
**Problem Statement:**
A sample is selected from a population with a mean (\(\mu\)) of 40 and a standard deviation (\(\sigma\)) of 8.
a. If the sample has \(n = 4\) scores, what is the expected value of \(M\) and the standard error of \(M\)?
b. If the sample has \(n = 16\) scores, what is the expected value of \(M\) and the standard error of \(M\)?
**Explanation:**
To solve this problem, we will use the following statistical concepts:
1. **Expected Value of \(M\):** This is equal to the population mean (\(\mu\)). Since the expected value measures the central location of the distribution of the sample mean, it remains the same as the population mean regardless of the sample size.
2. **Standard Error of \(M\):** This is calculated using the formula:
\[
\text{Standard Error of } M = \frac{\sigma}{\sqrt{n}}
\]
where \(\sigma\) is the standard deviation of the population, and \(n\) is the sample size. The standard error measures the variability of the sample mean around the population mean. It decreases as the sample size increases.
Expert Solution
Step 1
Given data:
Mean = 40
Standard deviation = 8
Step by step
Solved in 2 steps with 1 images
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