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
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Chapter1: Starting With Matlab
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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.
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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