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. **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 $

Given: Male Sample size (n1) = 100 Sample mean x¯1=57600 Sample standard deviation (s1) = 1000…

Answered: teachers and finds that among a random…

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

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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