Find the standardized test statistic t for a sample with n = 12, x = 18.8, s = 2.1, and a=0.01 if !3! Hai H #19.3. Round your answer to three decimal places. -0.037 -0.825 O -0.008 -0.381
Find the standardized test statistic t for a sample with n = 12, x = 18.8, s = 2.1, and a=0.01 if !3! Hai H #19.3. Round your answer to three decimal places. -0.037 -0.825 O -0.008 -0.381
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 Statement:**
Provide an appropriate response.
Find the standardized test statistic \( t \) for a sample with \( n = 12 \), \( \bar{x} = 18.8 \), \( s = 2.1 \), and \( \alpha = 0.01 \) if \( H_a: \mu \neq 19.3 \). Round your answer to three decimal places.
- \(-0.037\)
- \(-0.825\)
- \(-0.008\)
- \(-0.381\)
**Solution Explanation:**
To solve this problem, you need to calculate the t-statistic using the formula:
\[
t = \frac{\bar{x} - \mu}{s / \sqrt{n}}
\]
where:
- \(\bar{x} = 18.8\) is the sample mean,
- \(\mu = 19.3\) is the population mean under the null hypothesis,
- \(s = 2.1\) is the standard deviation of the sample,
- \(n = 12\) is the sample size.
Plug these values into the formula to find \( t \), and choose the closest value from the given options.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04103022-85df-4e59-af47-2e1159a1a031%2F24b0496e-1041-4193-96db-b4e3830d232e%2Fj3176ua_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Provide an appropriate response.
Find the standardized test statistic \( t \) for a sample with \( n = 12 \), \( \bar{x} = 18.8 \), \( s = 2.1 \), and \( \alpha = 0.01 \) if \( H_a: \mu \neq 19.3 \). Round your answer to three decimal places.
- \(-0.037\)
- \(-0.825\)
- \(-0.008\)
- \(-0.381\)
**Solution Explanation:**
To solve this problem, you need to calculate the t-statistic using the formula:
\[
t = \frac{\bar{x} - \mu}{s / \sqrt{n}}
\]
where:
- \(\bar{x} = 18.8\) is the sample mean,
- \(\mu = 19.3\) is the population mean under the null hypothesis,
- \(s = 2.1\) is the standard deviation of the sample,
- \(n = 12\) is the sample size.
Plug these values into the formula to find \( t \), and choose the closest value from the given options.
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