Claim: μ ≥ 8000; a=0.01 Sample statistics: x=7700, s=460, n=22 A. Ho: μ-8000 H₂: μ#8000 OC. Ho: #8000 H₂:μ=8000 *** B. Ho: 28000 H₂: μ< 8000 OD. Ho: ≤8000 H₂ μ>8000 What is the value of the standardized test statistic? The standardized test statistic is -3.06. (Round to two decimal places as needed.) What is the P-value? P= (Round to three decimal places as needed.)
Claim: μ ≥ 8000; a=0.01 Sample statistics: x=7700, s=460, n=22 A. Ho: μ-8000 H₂: μ#8000 OC. Ho: #8000 H₂:μ=8000 *** B. Ho: 28000 H₂: μ< 8000 OD. Ho: ≤8000 H₂ μ>8000 What is the value of the standardized test statistic? The standardized test statistic is -3.06. (Round to two decimal places as needed.) What is the P-value? P= (Round to three 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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![### T-Test for Population Mean
In this example, we aim to use a t-test to examine a claim about the population mean \( \mu \) at a specified significance level \( \alpha \). The provided sample statistics are used under the assumption that the population is normally distributed.
#### Given Information:
- Claim: \( \mu \geq 8000 \)
- Significance Level (\( \alpha \)): 0.01
- Sample Mean (\( \bar{x} \)): 7700
- Sample Standard Deviation (\( s \)): 460
- Sample Size (\( n \)): 22
#### Step-by-step Solution:
1. **Formulate the Hypotheses:**
- The null hypothesis (\( H_0 \)): \( \mu \geq 8000 \)
- The alternative hypothesis (\( H_a \)): \( \mu < 8000 \)
Choose the correct option based on the given claim:
- A. \( H_0 \): \( \mu = 8000 \), \( H_a \): \( \mu \neq 8000 \)
- B. \( H_0 \): \( \mu \geq 8000 \), \( H_a \): \( \mu < 8000 \) (selected)
- C. \( H_0 \): \( \mu \neq 8000 \), \( H_a \): \( \mu = 8000 \)
- D. \( H_0 \): \( \mu \leq 8000 \), \( H_a \): \( \mu > 8000 \)
2. **Calculate the Standardized Test Statistic:**
- The standardized test statistic (\( t \)) is calculated using the formula for the t-test:
\[
t = \frac{\bar{x} - \mu}{s / \sqrt{n}}
\]
Given:
\[
\bar{x} = 7700, \quad \mu = 8000, \quad s = 460, \quad n = 22
\]
Substitute the values:
\[
t = \frac{7700 - 8000}{460 / \sqrt{22}} = \frac{-300}{98.09} \approx -3.06
\]
The standardized test statistic is \( -3.06](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F952bcd3e-4a7c-474a-8dd6-ddd08471460a%2Fd4e57868-2d1c-4fda-ad65-aec790d9b0f8%2F0t2pxq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### T-Test for Population Mean
In this example, we aim to use a t-test to examine a claim about the population mean \( \mu \) at a specified significance level \( \alpha \). The provided sample statistics are used under the assumption that the population is normally distributed.
#### Given Information:
- Claim: \( \mu \geq 8000 \)
- Significance Level (\( \alpha \)): 0.01
- Sample Mean (\( \bar{x} \)): 7700
- Sample Standard Deviation (\( s \)): 460
- Sample Size (\( n \)): 22
#### Step-by-step Solution:
1. **Formulate the Hypotheses:**
- The null hypothesis (\( H_0 \)): \( \mu \geq 8000 \)
- The alternative hypothesis (\( H_a \)): \( \mu < 8000 \)
Choose the correct option based on the given claim:
- A. \( H_0 \): \( \mu = 8000 \), \( H_a \): \( \mu \neq 8000 \)
- B. \( H_0 \): \( \mu \geq 8000 \), \( H_a \): \( \mu < 8000 \) (selected)
- C. \( H_0 \): \( \mu \neq 8000 \), \( H_a \): \( \mu = 8000 \)
- D. \( H_0 \): \( \mu \leq 8000 \), \( H_a \): \( \mu > 8000 \)
2. **Calculate the Standardized Test Statistic:**
- The standardized test statistic (\( t \)) is calculated using the formula for the t-test:
\[
t = \frac{\bar{x} - \mu}{s / \sqrt{n}}
\]
Given:
\[
\bar{x} = 7700, \quad \mu = 8000, \quad s = 460, \quad n = 22
\]
Substitute the values:
\[
t = \frac{7700 - 8000}{460 / \sqrt{22}} = \frac{-300}{98.09} \approx -3.06
\]
The standardized test statistic is \( -3.06
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