parts a, b, and c please **Educational Content: Statistical Hypothesis Testing****Problem Statement:**Are couples that live together before they get married just as likely to end up divorced within five years of marriage compared to couples that live apart before they get married?- From the study: - 628 couples lived together before marriage, with 215 divorcing within five years. - 467 couples lived apart before marriage, with 123 divorcing within five years.**Objective:**Determine conclusions at the \(\alpha = 0.05\) level of significance.---**Steps for Hypothesis Testing:**1. **Select the Appropriate Test:** - Choose the test for comparing two proportions (e.g., Z-test for proportions).2. **Define Hypotheses:** - Null Hypothesis (\(H_0\)): The divorce rates are equal for both groups. - Alternative Hypothesis (\(H_1\)): The divorce rates are not equal for both groups. 3. **Test Statistic Calculation:** - Compute the test statistic (e.g., Z-value). Show your answer to three decimal places. 4. **P-value Calculation:** - Determine the p-value. Show the answer to four decimal places. 5. **Compare P-value and \(\alpha\):** - If \( p \leq \alpha \), reject \(H_0\). - If \( p > \alpha \), fail to reject \(H_0\).6. **Conclusion:** - Based on the comparison, decide to reject or not reject the null hypothesis.---**Decision Statements:**- **Option 1:** Results are statistically significant (\( p \leq \alpha \)), indicating different divorce rates for the two groups.- **Option 2:** Results are statistically insignificant (\( p > \alpha \)), indicating no evidence of different divorce rates.- **Option 3:** Statistically significant evidence for equal divorce rates.- **Option 4:** Statistically insignificant evidence for equal divorce rates.The final conclusion will be determined based on the calculations and comparison with \(\alpha = 0.05\).

Name: parts a, b, and c please **Educational Content: Statistical Hypothesis
Uploaded: 2024-03-05T11:53:49.000Z
Channel: Bartleby
Description: parts a, b, and c please **Educational Content: Statistical Hypothesis Testing****Problem Statement:**Are couples that live together before they get married just as likely to end up divorced within five years of marriage compared to couples that live

For this study we should use the two sample proportion z test. a. The null and alternative hypothesis are stated below: Null hypothesis: H0: p1 - p2 = 0 Alternative hypothesis: H1: p1 - p2 ≠0 b. The test statistics is obtained below: The sample proportion for p1-hat is, The sample proportion for p2-hat is, The test statistics formula is given below, Substitute 0.342 for p1-hat, 0.263 for p2-hat, n1 = 628 and n2 = 467 Thus, the test statistic (z) is 2.832. c. P-Value: It is given that, the level of significance is α = 0.05, test statistic (z) is 2.832. The excel formula for calculate the P-value is = 1-NORMDIST (x, mean standard_dev, cumulative) The P-value is: = 1-NORMDIST (2.832, 0, 1, 1) The P-value is 2 × 0.0023 = 0.0046. Thus, the p-value is 0.0046.