Listed below are the numbers of years that archbishops and monarchs in a certain country lived after their election or coronation. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a 0.05 significance level to test the claim that the mean longevity for archbishops is less than the mean for monarchs after coronation. All measurements are in years. Click the icon to view the table of longevities of archbishops and monarchs. What are the null and alternative hypotheses? Assume that population 1 consists of the longevity of archbishops and population 2 consists of the longevity of monarchs. OA. Ho: H1 H₂ H₁: Hy H₂ The test statistic is (Round to two decimal places as needed.) (Round to three decimal places as needed.) The P-value is State the conclusion for the test. OB. Ho: H₁ H₂ H₁ H₁ H₂ OD. Hoi Hạ#H H₁: Hy > H₂ idepoo to support the claim that archbishops have lower mean longevity than monarchs.
Listed below are the numbers of years that archbishops and monarchs in a certain country lived after their election or coronation. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a 0.05 significance level to test the claim that the mean longevity for archbishops is less than the mean for monarchs after coronation. All measurements are in years. Click the icon to view the table of longevities of archbishops and monarchs. What are the null and alternative hypotheses? Assume that population 1 consists of the longevity of archbishops and population 2 consists of the longevity of monarchs. OA. Ho: H1 H₂ H₁: Hy H₂ The test statistic is (Round to two decimal places as needed.) (Round to three decimal places as needed.) The P-value is State the conclusion for the test. OB. Ho: H₁ H₂ H₁ H₁ H₂ OD. Hoi Hạ#H H₁: Hy > H₂ idepoo to support the claim that archbishops have lower mean longevity than monarchs.
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Transcribed Image Text:**Analyzing Longevity: Archbishops vs. Monarchs**
In this educational exercise, we aim to understand if there is a significant difference in longevity between archbishops and monarchs after their election or coronation. For the purposes of this analysis, we will assume that we have two independent simple random samples from normally distributed populations. It is important to note that the population standard deviations are not assumed to be equal. We will use a 0.05 significance level to test the hypothesis that the mean longevity of archbishops is less than that of monarchs. All measurements are recorded in years.
**Hypothesis Testing**
**Given Information:**
- Population 1: Longevity of Archbishops.
- Population 2: Longevity of Monarchs.
- Significance Level: 0.05.
**Possible Hypotheses:**
Choose the correct set of null and alternative hypotheses:
- A. \(H_0: \mu_1 = \mu_2\) vs. \(H_1: \mu_1 < \mu_2\)
- B. \(H_0: \mu_1 = \mu_2\) vs. \(H_1: \mu_1 \neq \mu_2\)
- C. \(H_0: \mu_1 \leq \mu_2\) vs. \(H_1: \mu_1 > \mu_2\)
- D. \(H_0: \mu_1 \neq \mu_2\) vs. \(H_1: \mu_1 > \mu_2\)
**Test Statistic and P-value:**
Calculate and provide these values:
- The test statistic is: ____ (Round to two decimal places as needed.)
- The P-value is: ____ (Round to three decimal places as needed.)
**Conclusion:**
Based on the test statistic and P-value, state whether you would reject or fail to reject the null hypothesis:
- A. Reject the null hypothesis. There is not sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.
- B. Reject the null hypothesis. There is sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.
- C. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.
- D. Fail to reject
Transcribed Image Text:**Longevities of Archbishops and Monarchs**
The table below presents the longevity in years of Archbishops and Monarchs:
| | **1** | **2** | **3** | **4** | **5** | **6** | **7** | **8** | **9** | **10**| **11**| **12**| **13**| **14**| **15**| **16**| **17**| **18**| **19**| **20**| **21**| **22**|
|---------------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|
| **Archbishops**| 15 | 14 | 15 | 14 | 17 | 1 | 18 | 16 | 9 | 14 | 11 | 9 | | | | | | | | | | |
| **Archbishops**| 14 | 15 | 14 | 15 | 17 | 18 | 10 | 18 | 11 | 1 | 16 | 18 | | | | | | | | | | |
| **Monarchs** | 13 | 17 | 16 | 13 | 17 | 18 | 14 | 17 | 15 | 16 | 20 | 18 | | | | | | | | | | |
*Note: Each number represents the longevity (in years) of individual Archbishops and Monarchs.*
This dataset can be analyzed to understand the patterns and trends in the longevities of Archbishops and Monarchs over time.
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