An employment agency claims that the mean annual pay for full-time male workers over age 25 and without high school diplomas is $24,600. The annual pay for 10 full-time male workers over age 25 and without high school diplomas is shown below. $22,954 $23,438 $24,655 $23,695 $25,275 $19,212 $21,456 $25,493 $26,480 $28,585 Assume the distribution of the population is approximately normal. Test the claim using a=0.05. There is enough evidence to reject the null hypothesis. The claim is true. There is enough evidence to reject the null hypothesis. The claim is false. There is not enough evidence to reject the null hypothesis. The claim is probably true. There is not enough evidence to reject the null hypothesis. The claim is probably false.
An employment agency claims that the mean annual pay for full-time male workers over age 25 and without high school diplomas is $24,600. The annual pay for 10 full-time male workers over age 25 and without high school diplomas is shown below. $22,954 $23,438 $24,655 $23,695 $25,275 $19,212 $21,456 $25,493 $26,480 $28,585 Assume the distribution of the population is approximately normal. Test the claim using a=0.05. There is enough evidence to reject the null hypothesis. The claim is true. There is enough evidence to reject the null hypothesis. The claim is false. There is not enough evidence to reject the null hypothesis. The claim is probably true. There is not enough evidence to reject the null hypothesis. The claim is probably false.
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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![### Testing Claims About Mean Annual Pay
**Scenario:**
An employment agency claims that the mean annual pay for full-time male workers over age 25 and without high school diplomas is $24,600. The annual pay for 10 full-time male workers over age 25 and without high school diplomas is shown below:
| $22,954 | $23,438 | $24,655 | $23,695 | $25,275 |
|-----------|-----------|-----------|-----------|-----------|
| $19,212 | $21,456 | $25,493 | $26,480 | $28,585 |
Assume the distribution of the population is approximately normal. Test the claim using α=0.05.
**Choose the correct conclusion:**
- [ ] There is enough evidence to reject the null hypothesis. The claim is true.
- [ ] There is enough evidence to reject the null hypothesis. The claim is false.
- [ ] There is not enough evidence to reject the null hypothesis. The claim is probably true.
- [ ] There is not enough evidence to reject the null hypothesis. The claim is probably false.
### Explanation:
1. **State the Hypotheses**:
- Null Hypothesis (H0): μ = $24,600
- Alternative Hypothesis (H1): μ ≠ $24,600
2. **Calculate the Sample Mean (x̄)**:
- Summing the given values:
\( x = 22,954 + 23,438 + 24,655 + 23,695 + 25,275 + 19,212 + 21,456 + 25,493 + 26,480 + 28,585 \)
\( x = 241,243 \)
- Sample Size (n): 10
- Mean (x̄):
\( x̄ = \frac{x}{n} = \frac{241,243}{10} = 24,124.30 \)
3. **Calculate the Standard Deviation (s)**:
- Sample variance and then standard deviation can be calculated from individual data points.
4. **Determine the Standard Error (SE)**:
- \( SE = \frac{s}{\sqrt{n}} \), where \( s \) is the sample standard deviation.
5. **Calculate the Test Statistic (t)**:
- \( t = \frac{x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa14048f2-5cba-4f26-8479-4bf217c3ed07%2F700210ca-858e-46b5-86c1-960f9eb2ee64%2F86ghp_processed.png&w=3840&q=75)
Transcribed Image Text:### Testing Claims About Mean Annual Pay
**Scenario:**
An employment agency claims that the mean annual pay for full-time male workers over age 25 and without high school diplomas is $24,600. The annual pay for 10 full-time male workers over age 25 and without high school diplomas is shown below:
| $22,954 | $23,438 | $24,655 | $23,695 | $25,275 |
|-----------|-----------|-----------|-----------|-----------|
| $19,212 | $21,456 | $25,493 | $26,480 | $28,585 |
Assume the distribution of the population is approximately normal. Test the claim using α=0.05.
**Choose the correct conclusion:**
- [ ] There is enough evidence to reject the null hypothesis. The claim is true.
- [ ] There is enough evidence to reject the null hypothesis. The claim is false.
- [ ] There is not enough evidence to reject the null hypothesis. The claim is probably true.
- [ ] There is not enough evidence to reject the null hypothesis. The claim is probably false.
### Explanation:
1. **State the Hypotheses**:
- Null Hypothesis (H0): μ = $24,600
- Alternative Hypothesis (H1): μ ≠ $24,600
2. **Calculate the Sample Mean (x̄)**:
- Summing the given values:
\( x = 22,954 + 23,438 + 24,655 + 23,695 + 25,275 + 19,212 + 21,456 + 25,493 + 26,480 + 28,585 \)
\( x = 241,243 \)
- Sample Size (n): 10
- Mean (x̄):
\( x̄ = \frac{x}{n} = \frac{241,243}{10} = 24,124.30 \)
3. **Calculate the Standard Deviation (s)**:
- Sample variance and then standard deviation can be calculated from individual data points.
4. **Determine the Standard Error (SE)**:
- \( SE = \frac{s}{\sqrt{n}} \), where \( s \) is the sample standard deviation.
5. **Calculate the Test Statistic (t)**:
- \( t = \frac{x
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