12.A sample of n = 16 scores has a mean of M = 65 and an estimated standard error of 2 points. What is the sample variance? s2 = 64 c. s2 = 16 а. b. s2 = 36 d.s? = 4
12.A sample of n = 16 scores has a mean of M = 65 and an estimated standard error of 2 points. What is the sample variance? s2 = 64 c. s2 = 16 а. b. s2 = 36 d.s? = 4
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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![**Problem 12**
A sample of \( n = 16 \) scores has a mean of \( M = 65 \) and an estimated standard error of 2 points. What is the sample variance?
a. \( s^2 = 64 \)
b. \( s^2 = 36 \)
c. \( s^2 = 16 \)
d. \( s^2 = 4 \)
**Explanation**: The standard error (\(SE\)) is the standard deviation (\(s\)) of the sample distribution divided by the square root of the sample size (\(n\)). The formula to calculate the standard error is:
\[ SE = \frac{s}{\sqrt{n}} \]
Given that the standard error is 2, and \( n = 16 \), you can solve for \( s \) (standard deviation):
\[ 2 = \frac{s}{\sqrt{16}} \]
\[ 2 = \frac{s}{4} \]
\[ s = 8 \]
The sample variance (\(s^2\)) is the square of the standard deviation (\(s\)):
\[ s^2 = (8)^2 = 64 \]
Hence, the correct answer is \( a. \, s^2 = 64 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c8f01e2-a14e-48cc-8752-a6869fe4cc3e%2Fc6c283a1-bc78-4981-9738-cd3dd3aaccbf%2F5at1r7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 12**
A sample of \( n = 16 \) scores has a mean of \( M = 65 \) and an estimated standard error of 2 points. What is the sample variance?
a. \( s^2 = 64 \)
b. \( s^2 = 36 \)
c. \( s^2 = 16 \)
d. \( s^2 = 4 \)
**Explanation**: The standard error (\(SE\)) is the standard deviation (\(s\)) of the sample distribution divided by the square root of the sample size (\(n\)). The formula to calculate the standard error is:
\[ SE = \frac{s}{\sqrt{n}} \]
Given that the standard error is 2, and \( n = 16 \), you can solve for \( s \) (standard deviation):
\[ 2 = \frac{s}{\sqrt{16}} \]
\[ 2 = \frac{s}{4} \]
\[ s = 8 \]
The sample variance (\(s^2\)) is the square of the standard deviation (\(s\)):
\[ s^2 = (8)^2 = 64 \]
Hence, the correct answer is \( a. \, s^2 = 64 \).
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