Evaluate the following formula for x, = 97.65, x2 = 97.49, µ1 - 2 = 0, 01 =0.91, o2 = 0.65, n, = 12, and n2 = 47. (21 - 41) - (2x- x) n2 |(Round to two decimal places as needed.)
Evaluate the following formula for x, = 97.65, x2 = 97.49, µ1 - 2 = 0, 01 =0.91, o2 = 0.65, n, = 12, and n2 = 47. (21 - 41) - (2x- x) n2 |(Round to two decimal places as needed.)
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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![### Statistical Analysis Exercise
Evaluate the following formula for \( \overline{x}_1 = 97.65 \), \( \overline{x}_2 = 97.49 \), \( \mu_1 - \mu_2 = 0 \), \( \sigma_1 = 0.91 \), \( \sigma_2 = 0.65 \), \( n_1 = 12 \), and \( n_2 = 47 \).
\[
z = \frac{ \left( \overline{x}_1 - \overline{x}_2 \right) - \left( \mu_1 - \mu_2 \right) }{ \sqrt{ \frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2} } }
\]
### Given Values
- \( \overline{x}_1 = 97.65 \)
- \( \overline{x}_2 = 97.49 \)
- \( \mu_1 - \mu_2 = 0 \)
- \( \sigma_1 = 0.91 \)
- \( \sigma_2 = 0.65 \)
- \( n_1 = 12 \)
- \( n_2 = 47 \)
Calculate the \( z \)-score using the formula provided.
### Instructions
1. Substitute the given values into the formula.
2. Perform the arithmetic operations.
3. Round the final result to two decimal places.
\[
z = \frac{ (97.65 - 97.49) - 0 }{ \sqrt{ \frac{(0.91)^2}{12} + \frac{(0.65)^2}{47} } }
\]
\[
z = \frac{ 0.16 }{ \sqrt{ \frac{0.8281}{12} + \frac{0.4225}{47} } }
\]
\[
z = \frac{ 0.16 }{ \sqrt{ 0.0690083 + 0.0089894 } }
\]
\[
z = \frac{ 0.16 }{ \sqrt{ 0.0779977 } }
\]
\[
z = \frac{ 0.16 }{ 0.2793 }
\]
\[
z = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71d8e860-613e-4767-a1aa-a7e7c05fb956%2F3a640986-32c3-4074-876c-b10213e446df%2Fbg3jtkk.png&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis Exercise
Evaluate the following formula for \( \overline{x}_1 = 97.65 \), \( \overline{x}_2 = 97.49 \), \( \mu_1 - \mu_2 = 0 \), \( \sigma_1 = 0.91 \), \( \sigma_2 = 0.65 \), \( n_1 = 12 \), and \( n_2 = 47 \).
\[
z = \frac{ \left( \overline{x}_1 - \overline{x}_2 \right) - \left( \mu_1 - \mu_2 \right) }{ \sqrt{ \frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2} } }
\]
### Given Values
- \( \overline{x}_1 = 97.65 \)
- \( \overline{x}_2 = 97.49 \)
- \( \mu_1 - \mu_2 = 0 \)
- \( \sigma_1 = 0.91 \)
- \( \sigma_2 = 0.65 \)
- \( n_1 = 12 \)
- \( n_2 = 47 \)
Calculate the \( z \)-score using the formula provided.
### Instructions
1. Substitute the given values into the formula.
2. Perform the arithmetic operations.
3. Round the final result to two decimal places.
\[
z = \frac{ (97.65 - 97.49) - 0 }{ \sqrt{ \frac{(0.91)^2}{12} + \frac{(0.65)^2}{47} } }
\]
\[
z = \frac{ 0.16 }{ \sqrt{ \frac{0.8281}{12} + \frac{0.4225}{47} } }
\]
\[
z = \frac{ 0.16 }{ \sqrt{ 0.0690083 + 0.0089894 } }
\]
\[
z = \frac{ 0.16 }{ \sqrt{ 0.0779977 } }
\]
\[
z = \frac{ 0.16 }{ 0.2793 }
\]
\[
z = 0
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