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
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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 \( a. \, s^2 = 64 \).
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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