Question

Are couples that live together before they get married more likely to end up divorced within five years of marriage compared to couples that live apart before they get married? 208 of the 605 couples from the study who lived together before they got married were divorced within five years of marriage. 120 of the 428 couples from the study who lived apart before they got married were divorced within five years of marriage. What can be concluded at the  = 0.01 level of significance?

For this study, we should use Select an answer t-test for the difference between two dependent population means t-test for the difference between two independent population means t-test for a population mean z-test for a population proportion z-test for the difference between two population proportions

1. The null and alternative hypotheses would be:   
2.   

   Select an answer p1 μ1  Select an answer = < > ≠  Select an answer p2 μ2    

   Select an answer μ1 p1  Select an answer < ≠ = >  Select an answer p2 μ2

2. The test statistic ? z t  =  (please show your answer to 3 decimal places.)
3. The p-value =  (Please show your answer to 4 decimal places.)
4. The p-value is ? ≤ >  
5. Based on this, we should Select an answer fail to reject reject accept  the null hypothesis.
6. Thus, the final conclusion is that ...
   • The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the percent of the 605 couples that lived together before they got married who ended up divorced within five years of marriage is greater than the percent of the 428 couples that lived apart before they got married who ended up divorced within five years of marriage.
   • The results are statistically insignificant at αα = 0.01, so there is statistically significant evidence to conclude that the divorce rate for all couples that live together before they get married is equal to the divorce rate for all couples that live apart before they get married.
   • The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the percent of all couples that live together before they get married who end up divorced within five years of marriage is greater than the percent of all couples that live apart before they get married who end up divorced within five years of marriage.
   • The results are statistically insignificant at αα = 0.01, so there is insufficient evidence to conclude the percent of all couples that live together before they get married who end up divorced within five years of marriage is greater than the percent of all couples that live apart before they get married who end up divorced within five years of marriage.

Answer 1

The statistical software output for this problem is:

From above output:

a) Hypotheses:

Ho: p1 = p2

Ha: p1 ≠ p2

Test statistic = 2.157

P - value = 0.0310

P - value is greater than 0.01

We fail to reject the null hypothesis

Final conclusion: The results are statistically insignificant at αα = 0.01, so there is insufficient evidence to conclude the percent of all couples that live together before they get married who end up divorced within five years of marriage is greater than the percent of all couples that live apart before they get married who end up divorced within five years of marriage.