MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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a) Which of the following correctly specifies the null hypothesis? [select all that apply]
b) Which of the following correctly specifies the alternative hypothesis? [select all that apply]
c) Given the p-value you calculated (p
![### Hypothesis Testing in Teacher Salaries
#### Context:
A researcher investigates salaries of elementary school teachers. Among a random sample of 100 women teachers, the mean yearly salary is $57,600 with a standard deviation of $1,000. For a sample of 225 men teachers, the mean salary is $58,800 with a standard deviation of $1,100. Conduct a hypothesis test to assess the researcher’s claim.
#### Question:
Given the p-value you calculated, which of the following conclusions are correct for this test? (Select all that apply)
1. [ ] Because \( p > \alpha \), we fail to reject the null hypothesis.
2. [ ] There is support for the alternative hypothesis.
3. [ ] There is no support for the alternative hypothesis.
4. [ ] Because \( p < \alpha \), we can reject the null hypothesis.
5. [ ] This test suggests the researcher's hypothesis is incorrect.
6. [ ] This test supports the researcher's hypothesis.
#### Explanation of Choices:
- **\( p > \alpha \):** If the p-value is greater than the significance level \( \alpha \), the null hypothesis cannot be rejected.
- **\( p < \alpha \):** If the p-value is less than the significance level \( \alpha \), the null hypothesis is rejected.
- **Support for Hypotheses:** Depending on whether the null hypothesis is rejected or not, either the null or alternative hypothesis is supported.
Choose accordingly based on your calculated p-value and significance level.](https://content.bartleby.com/qna-images/question/e48de6f5-c24a-415a-97d6-6c6f62408c82/e81c8066-8c47-405c-9a3e-3f85dd640f18/4a73io1_processed.jpeg)
Transcribed Image Text:### Hypothesis Testing in Teacher Salaries
#### Context:
A researcher investigates salaries of elementary school teachers. Among a random sample of 100 women teachers, the mean yearly salary is $57,600 with a standard deviation of $1,000. For a sample of 225 men teachers, the mean salary is $58,800 with a standard deviation of $1,100. Conduct a hypothesis test to assess the researcher’s claim.
#### Question:
Given the p-value you calculated, which of the following conclusions are correct for this test? (Select all that apply)
1. [ ] Because \( p > \alpha \), we fail to reject the null hypothesis.
2. [ ] There is support for the alternative hypothesis.
3. [ ] There is no support for the alternative hypothesis.
4. [ ] Because \( p < \alpha \), we can reject the null hypothesis.
5. [ ] This test suggests the researcher's hypothesis is incorrect.
6. [ ] This test supports the researcher's hypothesis.
#### Explanation of Choices:
- **\( p > \alpha \):** If the p-value is greater than the significance level \( \alpha \), the null hypothesis cannot be rejected.
- **\( p < \alpha \):** If the p-value is less than the significance level \( \alpha \), the null hypothesis is rejected.
- **Support for Hypotheses:** Depending on whether the null hypothesis is rejected or not, either the null or alternative hypothesis is supported.
Choose accordingly based on your calculated p-value and significance level.
![**Scenario:** A researcher believes that elementary school teachers who are women earn less than their male counterparts. She collects data from elementary school teachers and finds that among a random sample of 100 teachers who are women, the mean yearly salary is $57,600 with a standard deviation of $1,000. The mean salary for a random sample of 225 elementary school teachers who are men is $58,800 with a standard deviation of $1,100. Conduct a hypothesis test to assess the researcher’s claim.
**Question:** Which of the following correctly specifies the **null** hypothesis? (select all that apply)
- [ ] \( H_0 : \mu_m - \mu_w = 0 \)
- [ ] There is no difference in the mean salaries of men and woman elementary school teachers.
- [ ] There is a difference in the mean salaries of men and woman elementary school teachers.
- [ ] \( H_0 : \mu_m - \mu_w \neq 0 \)
**Question:** Which of the following correctly specifies the **alternative** hypothesis? (select all that apply)
- [ ] There is no difference in the mean salaries of men and woman elementary school teachers.
- [ ] There is a difference in the mean salaries of men and woman elementary school teachers.
- [ ] \( H_0 : \mu_m - \mu_w \neq 0 \)
- [ ] \( H_0 : \mu_m - \mu_w = 0 \)](https://content.bartleby.com/qna-images/question/e48de6f5-c24a-415a-97d6-6c6f62408c82/e81c8066-8c47-405c-9a3e-3f85dd640f18/t7jvl7_processed.jpeg)
Transcribed Image Text:**Scenario:** A researcher believes that elementary school teachers who are women earn less than their male counterparts. She collects data from elementary school teachers and finds that among a random sample of 100 teachers who are women, the mean yearly salary is $57,600 with a standard deviation of $1,000. The mean salary for a random sample of 225 elementary school teachers who are men is $58,800 with a standard deviation of $1,100. Conduct a hypothesis test to assess the researcher’s claim.
**Question:** Which of the following correctly specifies the **null** hypothesis? (select all that apply)
- [ ] \( H_0 : \mu_m - \mu_w = 0 \)
- [ ] There is no difference in the mean salaries of men and woman elementary school teachers.
- [ ] There is a difference in the mean salaries of men and woman elementary school teachers.
- [ ] \( H_0 : \mu_m - \mu_w \neq 0 \)
**Question:** Which of the following correctly specifies the **alternative** hypothesis? (select all that apply)
- [ ] There is no difference in the mean salaries of men and woman elementary school teachers.
- [ ] There is a difference in the mean salaries of men and woman elementary school teachers.
- [ ] \( H_0 : \mu_m - \mu_w \neq 0 \)
- [ ] \( H_0 : \mu_m - \mu_w = 0 \)
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