Please show work 4. In social and behavioral sciences, the term \"Boomerang Gene
ID: 2948006 • Letter: P
Question
Please show work
4. In social and behavioral sciences, the term "Boomerang Generation" refers to the recent generation of young adults (ages 18-34) who have had to move back in with their parents. In a 2016 national survey, 200 out of 820 randomly selected young adults had to move back in with their parents. In a similar 2008 national survey, 140 out of 800 randomly selected young adults had to move back in with their parents. You, as a social scientist, would like to determine if there is a significant difference in the proportion of young adults who moved back in with their parents in 2016 and 2008?
SE=0.20236
Test Statistic (z) = 3.40
1. Calculate the p-value for the test. (show how found)
2. Assess the strength of your decision in part (1) using the p-value.
3. Calculate a 95% confidence interval for the difference between the two corresponding population proportions (see pages 280-281 in the Blue Book).
4. How does your result in part 3 relate to the decision regarding the null hypothesis in parts (1), 2), and the test statistic? Be specific.
Explanation / Answer
Solution1:
its a two tail test
Code inR to get p value
z <- 3.40
pval = 2 ? pnorm(z, lower.tail=FALSE)
pval
Output:
0.0006738585
p=0.0006738585
Solution2:
p<0.05
Reject null hypothesis.
Accept alternative hypothesis
There is sufficient evidence at 5% level of significance to conclude that there is a significant difference in the proportion of young adults who moved back in with their parents in 2016 and 2008.