Institution Military Religious Media/ Press DIF The contingency table shows how a random sample of college freshmen graded the leaders of three types of institutions. At a0.05, can you conclude that the grades are related to the institution? Complete parts (a) through (d) 21 19 24 39 42 42 23 21 13 22 37 27 (a) Identify the claim and state the null and alternative hypotheses. Họ: Grades are (1)– the institution. H, Grades are (2) the institution The (3)- is the claim (b) Determine the degrees of freedom, find the critical value, and identify the rejection region. What are the degrees of freedom? df= Find the critical value. (Round to three decimal places as needed) Choose the correct rejection region below. OB. > (c) Calculate the test statistic. If convenient, use technology (Round to three decimal places as needed) (d) Decide to reject or fal to reject the null hypothesis. Then interpret the decision in the context of the original claim. . Choose the corect conclusion below OA. Fail to reject the null hypothesis. There is enough evidence to conclude that grades are dependent on the institution. OC. Reject the null hypothesis. There is not enough evidence to conclude that grades are dependent on the institution. O B. Fail to reject the null hypothesis. There is not enough evidence to conclude that grades are dependent on the institution. OD. Reject the nul hypothesis. There is enough evidence to conclude that grades are dependent on the institution. (1) O independent of O dependent on (2) O independent of O dependent on (3) O alternative hypothesis O null hypothesis
Institution Military Religious Media/ Press DIF The contingency table shows how a random sample of college freshmen graded the leaders of three types of institutions. At a0.05, can you conclude that the grades are related to the institution? Complete parts (a) through (d) 21 19 24 39 42 42 23 21 13 22 37 27 (a) Identify the claim and state the null and alternative hypotheses. Họ: Grades are (1)– the institution. H, Grades are (2) the institution The (3)- is the claim (b) Determine the degrees of freedom, find the critical value, and identify the rejection region. What are the degrees of freedom? df= Find the critical value. (Round to three decimal places as needed) Choose the correct rejection region below. OB. > (c) Calculate the test statistic. If convenient, use technology (Round to three decimal places as needed) (d) Decide to reject or fal to reject the null hypothesis. Then interpret the decision in the context of the original claim. . Choose the corect conclusion below OA. Fail to reject the null hypothesis. There is enough evidence to conclude that grades are dependent on the institution. OC. Reject the null hypothesis. There is not enough evidence to conclude that grades are dependent on the institution. O B. Fail to reject the null hypothesis. There is not enough evidence to conclude that grades are dependent on the institution. OD. Reject the nul hypothesis. There is enough evidence to conclude that grades are dependent on the institution. (1) O independent of O dependent on (2) O independent of O dependent on (3) O alternative hypothesis O null hypothesis
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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![**Contingency Table Analysis - Institutional Impact on Grades**
The contingency table below illustrates how a random sample of college freshmen graded the leaders of three types of institutions. At a significance level of α = 0.05, we need to assess whether grades are related to the institution type.
| Institution | A | B | C | D/F |
|---------------|----|----|----|-----|
| Military | 39 | 42 | 23 | 21 |
| Religious | 21 | 42 | 22 | 19 |
| Media / Press | 13 | 27 | 37 | 24 |
**Steps to Analyze:**
**(a) Identify Hypotheses:**
- Null Hypothesis (\(H_0\)): Grades are (independent) of the institution.
- Alternative Hypothesis (\(H_a\)): Grades are (dependent) on the institution.
**(b) Determine Degrees of Freedom, Critical Value, and Rejection Region:**
- Degrees of Freedom: \(d.f. = (3-1)(4-1) = 6\)
- Find the critical value for \( \chi^2 \) at \(d.f. = 6\) and \(\alpha = 0.05\).
- Choose the correct critical region:
- A. \( \chi^2 \leq \chi_0^2 \)
- B. \( \chi^2 > \chi_0^2 \)
- C. \( \chi^2 \leq \chi_0^2 \)
- D. \( \chi^2 > \chi_0^2 \)
**(c) Calculate the Test Statistic:**
- \(\chi^2 =\) [Round to three decimal places as needed.]
**(d) Decision and Conclusion:**
- Decide based on test statistic and critical value.
- Choose the conclusion:
- A. Fail to reject \(H_0\). There is enough evidence to conclude that grades are dependent on the institution.
- B. Fail to reject \(H_0\). There is not enough evidence to conclude that grades are dependent on the institution.
- C. Reject \(H_0\). There is not enough evidence to conclude that grades are dependent on the institution.
- D. Reject \(H_0\). There is enough](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcbd6a68d-f6ca-4106-a572-576a83876ff9%2F632ae0fe-446a-47ed-b5f6-ae18beaae8a9%2Fl1qlpdn_processed.png&w=3840&q=75)
Transcribed Image Text:**Contingency Table Analysis - Institutional Impact on Grades**
The contingency table below illustrates how a random sample of college freshmen graded the leaders of three types of institutions. At a significance level of α = 0.05, we need to assess whether grades are related to the institution type.
| Institution | A | B | C | D/F |
|---------------|----|----|----|-----|
| Military | 39 | 42 | 23 | 21 |
| Religious | 21 | 42 | 22 | 19 |
| Media / Press | 13 | 27 | 37 | 24 |
**Steps to Analyze:**
**(a) Identify Hypotheses:**
- Null Hypothesis (\(H_0\)): Grades are (independent) of the institution.
- Alternative Hypothesis (\(H_a\)): Grades are (dependent) on the institution.
**(b) Determine Degrees of Freedom, Critical Value, and Rejection Region:**
- Degrees of Freedom: \(d.f. = (3-1)(4-1) = 6\)
- Find the critical value for \( \chi^2 \) at \(d.f. = 6\) and \(\alpha = 0.05\).
- Choose the correct critical region:
- A. \( \chi^2 \leq \chi_0^2 \)
- B. \( \chi^2 > \chi_0^2 \)
- C. \( \chi^2 \leq \chi_0^2 \)
- D. \( \chi^2 > \chi_0^2 \)
**(c) Calculate the Test Statistic:**
- \(\chi^2 =\) [Round to three decimal places as needed.]
**(d) Decision and Conclusion:**
- Decide based on test statistic and critical value.
- Choose the conclusion:
- A. Fail to reject \(H_0\). There is enough evidence to conclude that grades are dependent on the institution.
- B. Fail to reject \(H_0\). There is not enough evidence to conclude that grades are dependent on the institution.
- C. Reject \(H_0\). There is not enough evidence to conclude that grades are dependent on the institution.
- D. Reject \(H_0\). There is enough
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