Question

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?
(a) State the research question.

Is there is a significant difference in the proportion of young adults who moved back in with their parents in 2016 and 2008?
(b) State both the null and alternative hypotheses.

(c) Determine the critical values (use 5% significance level).

(d) Calculate the standard error (see page 160 in the Pineapple Book).

SE=0.020236

(d) Calculate the test statistic, and state the decision regarding the null hypothesis

z=3.40

(e) Calculate the p-value for the test.

(f) Assess the strength of your decision in part (d) using the p-value.

We reject the null hypothesis. Since the p-value is very low, the observed difference is said to be highly statistically significant.
(g) Answer the research question. How would you describe current trend?

There is a highly significant difference between the proportion of young adults who moved back in with their parents in 2016, and 2008.
(h) Calculate a 95% confidence interval for the difference between the two corresponding population proportions (see pages 280-281 in the Blue Book).

(i) How does your result in part (h) relate to the decision regarding the null hypothesis in parts (d), (e), and (f)? Be specific.

I was wondering if you could help show how the p-value is calculated from the data listed, and I was also wondering if I could get some assistance with part h and i? Thank you in advance

1

1

Answer 1

a) Is there significant difference in the proportion of young adults moving back with parents over the years? : Research question

b) Null hypothesis -> H0 : No difference in proportion
ALternative hypothesis > H1 : not H0

c) Critical value : X²_0.05;1 = 7.88

e)R code and output :

> tab=matrix(c(140,800-140,200,620),nrow=2,byrow=T)
> rownames(tab)=c("2008","2016")
> colnames(tab)=c("Move back","Did not move back")
> tab=as.table(tab)
> tab
Move back Did not move back
2008 140 660
2016 200 620
> chisq.test(tab)

Pearson's Chi-squared test with Yates' continuity correction

data: tab
X-squared = 11.181, df = 1, p-value = 0.0008263

Since p-value is very small, we reject the null hypothesis and conclude that there is significant difference in the proportion of young adults moving back over the years.